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v4.1
a
Acknowledgments
The following people deserve thanks for their help with this book:
Many thanks to John Fulmer, National Content Director for the GRE,
Kyle Fox, and Terry Serres for their hard work revising the 2018
edition.
The Princeton Review would also like to give a special thank-you to
Jim Havens for his dedication and leadership in coordinating this
project, as well as the following top-notch contributors: Chris Benson,
Marty Cinke, Kevin Kelly, Sara Kuperstein, and Derek Smith.
Special thanks to Adam Robinson, who conceived of and perfected the
Joe Bloggs approach to standardized tests, and many of the other
successful techniques used by The Princeton Review.
Contents
Cover
Title Page
Copyright
Acknowledgments
Register Your Book Online!
Part I: Orientation
1
Introduction
2
General Strategy
Part II: How to Crack the Verbal Section
3
The Geography of the Verbal Section
4
Text Completions
5
Sentence Equivalence
6
Reading Comprehension
7
Critical Reasoning
8
Vocabulary for the GRE
Part III: How to Crack the Math Section
9
The Geography of the Math Section
10
Math Fundamentals
11
Algebra (And When to Use It)
12
Real World Math
13
Geometry
14
Math Et Cetera
Part IV: How to Crack the Analytical Writing Section
15
The Geography of the Analytical Writing Section
16
The Issue Essay
17
The Argument Essay
Part V: Answers and Explanations to Drills and Practice Sets
Part VI: Practice Tests
18
Practice Test 1
19
Practice Test 1: Answers and Explanations
20
Practice Test 2
21
Practice Test 2: Answers and Explanations
Appendix: Accommodated Testing
GRE Insider
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2
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3
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4
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Part I
Orientation
1
Introduction
2
General Strategy
Chapter 1
Introduction
What is the GRE? Who makes the test? What’s a good score? The answer to
these questions and many others lie within this chapter. In the next few pages,
we’ll give you the lowdown on the things you need to know about the GRE.
CRACKING THE GRE
For a lot of people, taking a standardized test such as the GRE usually
engenders a number of emotions—none of them positive. But here’s the good
news: The Princeton Review is going to make this whole ordeal a lot easier
for you. We’ll give you the information you will need to do well on the GRE,
including our time-tested strategies and techniques.
A few years back, the GRE was rather significantly revised. This “new”
version of the test supposedly allows graduate schools to get a better sense of
an applicant’s ability to work in a post-graduate setting—a goal that is
unrealistic indeed, considering that the people who take the GRE are applying
to programs as diverse as physics and anthropology.
Strategies Galore
In this book you’ll find The
Princeton Review’s trusted
test-taking strategies to
help you crack the GRE.
However, it’s safe to say that neither GRE—new or old—is a realistic
measure of how well you’ll do in grad school, or even how intelligent you
are. In fact, the GRE provides a valid assessment of only one thing:
The GRE assesses how well you take the GRE.
Got it? Even so, you still want to do well on the GRE, because you want grad
schools to take you seriously when they consider your application. With this
in mind, you should cultivate several very important skills when you’re
preparing for the test; each of them is attainable with the right guidance
(which we’ll give you), a strong work ethic (which you must provide), and a
healthy dose of optimism. Who knows? Maybe after working through this
book and learning how to crack the test, you’ll actually look forward to taking
the GRE.
So what exactly is this test you’ve heard so much about?
WHAT IS THE GRE?
The Graduate Record Examination (GRE) is a 3-hour, 45-minute exam that’s
used to rank applicants for graduate schools. The scored portion of the GRE
consists of the following sections:
•
One 30-minute Analysis of an Issue essay
•
One 30-minute Analysis of an Argument essay
•
Two 30-minute Verbal Reasoning sections
•
Two 35-minute Quantitative Reasoning sections
The Verbal Reasoning sections test your skills on three different types of
questions:
•
Text Completion
•
Sentence Equivalence
•
Reading Comprehension
The Quantitative Reasoning sections measure your prowess in four areas:
•
Arithmetic and Number Properties
•
Algebra
•
Geometry
•
Data Analysis
Fun fact: It’s possible your
GRE score could come in
handy if you are interested
in law school. Check
a school’s admissions
page for more info, as
some schools are (or are
considering) accepting
GRE scores in lieu of LSAT
scores. Your grad school
options may have opened
up even further!
WHY DO SCHOOLS REQUIRE IT?
Even though you will pay ETS $205 to take the GRE, it is important to note
that you are not their primary customer. Their primary customers are the
admissions offices at graduate programs across the United States. ETS
provides admissions professionals with two important services. The first is a
number, your GRE score. Everyone who takes the test gets a number. It is
difficult for admissions committees to make a decision between a candidate
with a 3.0 and a 3.2 GPA from drastically different schools and in two
different majors. A GRE score, on the other hand, provides a quick and easy
way for busy admissions offices to whittle a large applicant pool down to size.
Applicants could come from all over the world and will certainly have an
enormous range in academic and professional experience. How does one
compare a senior in college with a 32-year-old professional who has been out
of college working in a different industry for the past 10 years? A GRE score
is the only part of the application that allows for an apples-to-apples
comparison among all applicants.
The second service that ETS provides is mailing lists. That’s right; they will
sell your name. You can opt out, but when you sit down to take the test, ETS
will ask you a whole bunch of questions about your educational experience,
family background, race, and gender, as well as other biographical data. All of
this information goes into their database. In fact, ETS is one of the most
important sources of potential applicants that many graduate programs have.
Another reason schools require the GRE is that it ensures that most graduate
school applicants are qualified. It helps to weed out the people who might be
considering grad school, but who can’t get their act together enough to fill out
applications. When you ask a program how important the GRE score is to the
application, they may say, “it depends” or “not very” and that may be true as
long as your score is in the top half. If your score is in the bottom half,
however, it may mean that your application never gets seen.
So the GRE may have little relevance to any particular field of study you
might be pursuing, but as long as it helps graduate programs uncover potential
candidates, and as long as it is the only tool available to compare a diverse
candidate pool, the GRE is here to stay.
WHO IS ETS?
Like most standardized tests in this country, the GRE is created and
administered by Educational Testing Service (ETS), a private company
located in New Jersey. ETS publishes the GRE under the sponsorship of the
Graduate Record Examinations Board, which is an organization affiliated
with the Association of Graduate Schools and the Council of Graduate
Schools in the United States.
ETS is also the organization that brings you the SAT, the Test of English as a
Foreign Language (TOEFL), the National Teacher Examination (NTE), and
licensing and certification exams in dozens of fields, including hair styling,
plumbing, and golf.
TEST DAY
The GRE is administered at Prometric testing centers. This company
specializes in administering tests on computer. They administer citizenship
exams, professional health certifications, dental exams, accounting exams,
and hundreds of other exams on computer. When you arrive at the center, they
will check your ID, give you a clipboard with a form to fill out, and hand you
a locker key. Despite the fact that they already have your information, you
will be asked to fill out a long form on paper. This form includes an entire
paragraph that you have to copy over—in cursive (they specify this)—that
states that you are who you say you are and that you are taking the test for
admissions purposes. This process will take you about 10 minutes, and you
can complete it while you wait for them to call you into the testing room. The
locker is for all of your personal belongings, including books, bags, phones,
bulky sweaters, and even watches. You are not allowed to take anything with
you into the testing room.
When they call you into the testing room, they will first take a photo of you
and, in some cases, fingerprint you before you go in. They will give you six
sheets of scratch paper, stapled together to form a booklet, and two sharpened
pencils with erasers. Then they lead you into the room where someone will
start your test for you. The room itself will hold three or four rows of standard
corporate cubicles, each with a monitor and keyboard. There will be other
people in the room taking tests other than the GRE. Because people will be
entering and exiting the room at different times, you will be provided with
optional headphones.
What to Take to
the Test Center:
1. Your registration ticket
2. A photo ID and one
other form of ID
3. A snack
Test Day Tips
•
Dress in layers, so that you’ll be comfortable regardless of whether
the room is cool or warm.
•
Don’t bother to take a calculator; you’re not allowed to use your
own—just the one on the screen.
•
Be sure to have breakfast, or lunch, depending on when your test
is scheduled (but don’t eat anything weird). Take it easy on the
liquids and the caffeine.
•
Do a few GRE practice problems beforehand to warm up your
brain. Don’t try to tackle difficult new questions, but go through a
few questions that you’ve done before to help you review the
problem-solving strategies for each section of the GRE. This will
also help you put on your “game-face” and get you into test mode.
•
Make sure to take photo identification to the test center.
Acceptable forms of identification include your driver’s license,
photo-bearing employee ID cards, and valid passports.
•
If you registered by mail, you must also take the authorization
voucher sent to you by ETS.
•
Stretch, drink some water, go to the bathroom, and do whatever
you need to do in order to be prepared to sit for this four-hour test.
TEST STRUCTURE
While your test structure may vary, you should expect to see something like
this when you sit down to take the exam:
The first section of the test collects all of your biographical information. If
you fill this out, you will start getting mail from programs that have bought
your name from ETS. In general, this is not a bad thing. If you don’t want
them to sell your name, or you don’t want to spend the time answering their
questions, you can click on a box that tells ETS not to share your information.
Once all of that is done, you will begin your first scored section, the essays.
The two essays will be back to back. You have 30 minutes for each essay.
Immediately after your second essay, you will get your first multiple-choice
section. It may be math or verbal. You will have a 1-minute break between
sections. Here is the structure of the test:
Section
Time
# of
Questions
Biographical
Information
+/− 10 minutes
−
Issue Essay
30 minutes
1
Argument Essay
30 minutes
1
Section 1
30 or 35
minutes
20
Section 2
30 or 35
minutes
20
Break
10 minutes
−
Section 3
30 or 35
minutes
20
Section 4
30 or 35
minutes
20
Section 5
30 or 35
minutes
20
Possible Research
Section
Optional
Depends
Select
Schools/Programs
5 minutes
Up to 4
Accept Scores
1 minute
−
Receive Scores
1 minute
−
More Online
For tons of information
about the GRE, check out
PrincetonReview.com/
grad/gre-information
Here are some things to keep in mind:
•
You will see five multiple-choice sections, but only four will
count. The fifth is an “experimental” section. It can come at any
time after the essays. At the end of the exam, you will know, based
on the number of math or verbal sections, if the experimental
section was math or verbal, but you will not know which section
will not count toward your score.
•
Math sections are 35 minutes. There are 20 math questions in each
section. If your experimental section is math, your test will be five
minutes longer than someone whose experimental section is
verbal.
•
Verbal sections are 30 minutes. There are 20 verbal questions in
each section.
•
For the computer-delivered test, the optional 10-minute break
comes after the second multiple-choice section. For the paperbased test, the 10-minute break comes after the second Analytical
Writing section.
•
You may or may not get a research section. If you do, it will come
last; it does not count toward your score, and it is optional.
•
You must accept your scores and, if you choose, send your scores
to selected programs prior to seeing your scores.
•
If you choose not to accept your scores, neither you nor any
program will ever see them.
•
You may choose to send your scores to up to four graduate
programs on the day of the test. This service is included in your
testing fee.
A Note on the
Paper-Based GRE
The computer-delivered
GRE is the standard
format for test takers. The
paper-based GRE is far
more rare and only offered
up to three times a year.
But if you want to learn
more about the paper-andpencil test, visit ETS.org.
The Experimental Section
ETS administers the experimental section to gather data on questions before
they appear on real GREs. You will have no way of knowing in advance
which multiple-choice section is experimental, so you need to do your best on
all of them. Don’t waste time worrying about which sections count and which
section does not.
Research Section
At the end of the test, you may also have an unscored research section. At the
beginning of this section, you will be told that it is an unscored research
section, and that it will be used only to help develop and test questions for the
GRE. You have the option to skip it if you want. You may be offered some
sort of prize to induce you to take it, but by that point in the test you will
probably be exhausted. If you’re offered a research section, just go ahead and
decline, get your scores, and go home.
The 10-Minute Break
You are given 1 minute between sections except for the second multiplechoice section, when you get a 10-minute break. Go to the bathroom, splash
water on your face, wave your arms around. You want to re-oxygenate your
brain. The goal, as much as it is possible, is to hit your brain’s reset button.
When you sit back down for the third multiple-choice section, you want to
feel as if you are just sitting down at that computer for the first time that day.
Your GRE test day is going to be a long and intense day, so be sure to take
full advantage of break time.
Practice Like You Play
When tackling practice
tests during your test
preparation, be sure to
mimic the real GRE and
give yourself these timed
breaks just like the real
thing.
Accepting Your Scores
Before you see your scores, you will be given the opportunity to cancel them.
There are very few reasons to do so. First, if you cancel your scores, you will
never see them and you will have to go through the whole experience again,
including paying an additional $205 to take the test again. Second, GRE
scores are curved. Most people believe that they are doing worse while taking
the test than they actually are. Third, you can make use of the GRE
ScoreSelect® service.
ScoreSelect®
ScoreSelect® allows you to select which scores get sent to which schools.
Options for sending scores depend on whether you are sending scores on the
day of your test or after your test day. On test day, you have the following
options for sending scores:
•
Most recent. This option sends the results of the test you just
took.
•
All. This option sends all your scores from the last five years.
If you send your scores to schools after test day, you have even more options.
After test day, your options are:
•
Most recent. This option sends the scores from the test you took
most recently.
•
All. As above, this option sends all your GRE scores from the last
five years.
•
Any. Send just the scores you want to send. You can send one
score or multiple scores. For example, if you have taken the GRE
three times and your second score is your best, you can send just
that score.
When you use ScoreSelect® after your test day, the score report that is sent to
schools shows only the scores that you choose to send. The report does not
indicate how many times you have taken the GRE nor does it indicate which
that you have sent, for example, the second of three scores on record.
ScoreSelect® is another reason to think twice before cancelling your scores.
Provided that you send your scores after your test date, your schools will
never know that you didn’t do as well as you would have liked or even that
you took the test more than once if you don’t want them to know.
Sending Additional Score Reports
On the day of your test, you can send your scores to up to four schools using
the ScoreSelect® test day options. These score reports are included as part of
the $205 fee that you pay to take the GRE. If you wish to send reports to
additional schools, you’ll need to request that these additional reports be sent
after your test day. Each additional report costs $27. The fastest way to send
additional score reports is to order them online using your My GRE® account
that you create when you register to take the test.
WHAT DOES A GRE SCORE LOOK LIKE?
Every GRE score has two components: a scaled score and a percentile rank.
GRE scores fall on a 130–170 point scale. However, your percentile rank is
more important than your scaled score. Your percentile rank indicates how
your GRE scores compare to those of other test takers. For example, a scaled
score of 150 on the GRE translates to roughly the 43rd percentile, meaning
that you scored better than 43 out of every 100 test takers—and worse than
the other 57 percent of test takers. A score of 152 is about average, while
scores of 163 and above are very competitive. Get the latest reported scores
and percentiles at PrincetonReview.com and at www.ets.org/gre, the official
ETS website for the GRE.
Plenty o’ Practice Tests
Head over to your
Premium Portal to gain
access to online practice
tests that include detailed
score reports. These score
reports can help guide
and focus your test
preparation time.
The essays are scored a little differently than the Verbal and Quantitative
sections. All essays receive a scaled score of 0–6, in half-point increments.
The corresponding percentiles are as follows:
Score
Analytical Writing Percentile
6.0
99
5.5
97
5.0
93
4.5
78
4.0
54
3.5
35
3.0
14
2.5
6
2.0
2
1.5
1
1.0
<1
In other words, a score of 5 on the essay portion of the GRE means you
performed better than 93 percent of test takers.
Grad School Info
Our Princeton Review
homepage has tons of
informational articles
about graduate
school. Head over to
PrincetonReview.com/
grad-school-advice and
check them out! Also
check out the GRE Insider
at the end of this book
for even more admissions
guidance and need-toknow info.
How Much Does the GRE Matter?
Some programs consider the GRE very important, while others view it as
more of a formality. Because the GRE is used for such a wide range of
graduate studies, the relative weight it is given will vary from field to field
and from school to school. A master’s program in English literature will not
evaluate the GRE the same way as a PhD program in physics, but it’s hard to
predict what the exact differences will be. A physics department may care
more about the Math score than the Verbal score, but given that nearly all of
its applicants will probably have high Math scores, a strong Verbal score
might make you stand out and help you gain admission.
Do Your Research
GRE scores are used in a number of different ways. The first step in figuring
out how to prepare for the GRE is figuring out how your scores will be used.
The only way to do that is to contact the programs to which you plan to apply.
Larger programs may have many of these questions already spelled out on
their websites. Smaller programs, on the other hand, may not want to be
pinned down to specific answers, and the answers may change from year to
year. If you are applying to a smaller program, you will have to dig a bit
deeper to get answers to some of these questions. Here are some things you
should be asking.
1. What scores do I need to be accepted? The answer to this
question is always “It depends.” The GRE is not the only part of
the application, and the quality of the applicant pool varies from
year to year. Nevertheless, you need to have a target score so you
can figure out how much work you need to put in between now and
test day. If the school doesn’t have or won’t quote you a cutoff
score, see if you can at least find out the average scores for last
year’s incoming class.
2. Will you look at all parts of my score? Some programs may care
about your math score, but not your verbal score, and vice versa.
Many programs don’t use the essay scores at all. If a program
doesn’t care about your math or your essay score, then you know
exactly where to put your prep time.
3. Are scores used for anything else? If your scores are to be used
for placement or for scholarship, it would be good to know that
now, while you still have time to prepare.
4. How important are my scores? In many ways, the importance of
scores is a function of how competitive the program is. The scores
may not matter much, but if it is a competitive program, every
number will count.
5. What do you do with multiple scores? Depending upon your first
scores, you may have to take the test a second time. It would be
good to know, however, the importance of that first score. If a
school is going to take the highest score, then you can relax a bit on
test one, knowing that you can take it again if you need to.
If you plan your testing schedule well, you can send only your highest scores
to the school using ScoreSelect®. Remember, however, that you must send
your scores after your test day to use the select any option for ScoreSelect®.
In any case, remember that the GRE is only one part of an application to grad
school. Admissions officers also consider many other factors, including
•
undergraduate transcripts (that is, your GPA, relevant courses, and
the quality of the school you attended)
•
work experience
•
any research or work you’ve done in that academic field
•
subject GREs (for certain programs)
•
essays (Personal Statements or other essays)
•
recommendations
•
interviews
The GRE can be a significant part of your graduate school application (which
is why you bought this book), but it certainly isn’t the only part.
Premium Portal
Head over to your
Premium Portal for tons
of pre-graduate school
information and guidance.
SCHEDULING A TEST
You can schedule a test session for the GRE by calling 800-GRE-CALL or by
registering online at www.ets.org/gre. Registering online is the easiest way to
register. As part of the registration process, you’ll create a MyGRE® account.
The account will also allow you to see your scores online and make use of the
GRE Diagnostic Service, which will give you some insight into your
performance. You can also register through a local testing center (the list of
centers is available online). After you get the list of local testing centers from
ETS, you can call the one nearest you and set up an appointment. You can
also call ETS at 609-771-7670 or e-mail them directly at their website to ask
any general questions you have about the GRE.
Computer Testing Facts
•
You can take the GRE almost any day—morning or afternoon,
weekday or weekend. Appointments are scheduled on a firstcome, first-served basis. You may take the test only once every 21
days. In addition, you cannot take the test more than five times in a
continuous rolling 12-month period. Make sure to take your test
early enough to book a second test date, if needed, before your
applications are due.
•
There’s no real deadline for registering for the test (technically,
you can register the day before). But there’s a limited number of
seats available on any given day and centers do fill up, sometimes
weeks in advance. It’s a good idea to register in advance, to give
yourself at least a couple of weeks of lead time.
•
The GRE is technically simple. Selecting an answer and moving to
the next question involves three easy steps. All you need to do is
point the mouse arrow at the answer and click, then click the
“Next” button, and then click the “Answer Confirm” button to
confirm your choice.
•
Because the test is administered on a computer, it is impossible to
write directly on the problems themselves (to underline text, cross
out answer choices, and so on). Thus, all of your work must be
done on scratch paper. Although the amount of scratch paper you
may use is unlimited, requesting additional paper takes time. You
should be efficient and organized in how you use it; learning to use
your scratch paper effectively is one of the keys to scoring well on
the GRE.
•
When you’ve finished taking the test, you will be given the option
to accept or cancel your scores. Of course, you have to make this
decision before you learn what the scores are. If you choose to
cancel your scores, they cannot be reinstated, and you will never
learn what they were. No refunds are given for canceled scores,
and your GRE report will reflect that you took the test on that day
and canceled (though this shouldn’t be held against you). If you
choose to accept your scores, they cannot be canceled afterward.
We suggest that unless you are absolutely certain you did poorly,
you accept your score.
•
You will receive your Verbal and Math scores the instant you
finish the exam (provided that you choose not to cancel your
score), but your Analytical Writing scores and “official” percentile
scores for all three sections won’t get to you until a few weeks
later. If you registered for your test online, you’ll be able to access
your official scores through your My GRE® account.
•
ETS offers the GRE® Diagnostic Service (grediagnostic.ets.org)
as a free option for test takers to have a limited review of their
tests. This service allows you to see the number of questions you
missed and where they fell on the test, but you cannot review the
actual questions. The diagnostic service also claims to let you
know the difficulty of the questions you missed, but the scale used
—a simple scale of 1 to 5—is not particularly useful.
Accommodated Testing
If you require accommodated testing, please see the Appendix at the end of
this book. It contains information on the forms you’ll need to fill out and
procedures you’ll need to follow to apply for accommodated testing. Be sure
to start that application process well in advance of when you want to take
your test, as it can take many weeks to complete.
HOW TO USE THIS BOOK
This book is chock full of our tried-and-true GRE test-taking techniques,
some of which, at first, might seem to go against your gut instincts. In order
to take full advantage of our methods, however, you’ll have to trust them and
use them consistently and faithfully.
Make sure to use the techniques on all of the practice problems you do and to
thoroughly review the explanations for all of the questions—even the ones
you get right. That way, the techniques will become second nature to you, and
you’ll have no problem using them on test day.
Trust in the Techniques
What makes The
Princeton Review’s test
prep so unique are our
powerful test-taking
strategies. Trust them and
use them faithfully, and
you won’t be disappointed!
Practice for Technique
There is a finite amount of GRE material available in the world. Once you
have used it all up, that’s it. You don’t get any more. Many people will work
through the books, doing problems, looking for answers. When they get a
problem right, they are happy. When they get a problem wrong, they are
frustrated, and then they go on to the next problem. The problem with this
approach is that you can churn through lots and lots of questions without ever
actually getting better at taking the GRE. The techniques you use and the way
you solve a problem are what matters. The results just tell you how you did.
When you are practicing, always focus on your approach. When you get good
at the techniques, your score will take care of itself. If you focus on just the
results, you do nothing more than reinforce the way you are taking the test
right now.
Additional Resources
In addition to the material in the book, we offer a number of other resources
to aid you during your GRE preparation.
With your purchase of this book, you gain access to many helpful tools in
your Premium Portal, which is the companion website that goes with this
book. There you will find four full-length practice GRE exams, assorted
videos in which Princeton Review teachers discuss GRE question types and
strategies, plus tons of useful articles, essays, and information. Go to
PrincetonReview.com/cracking to register. PrincetonReview.com/gre also
contains a ton of useful information on graduate programs, financial aid, and
everything else related to graduate school.
Extra Prep in Your
Premium Portal
Follow the steps on the
Register Your Book Online!
page to access
the Premium Portal and
find a bunch of great
content designed to boost
your test prep.
Real GREs
The practice problems in this book are designed to simulate the questions that
appear on the real GRE. Part of your preparation, however, should involve
working with real GRE problems. Working with real questions from past
GRE exams is the best way to practice our techniques and prepare for the test.
However, the only source of real GREs is the publisher of the test, ETS,
which so far has refused to let anyone (including us) license actual questions
from old tests.
Therefore, we strongly recommend that you obtain POWERPREP® II
software for the computer-based GRE revised General Test. You can
download the POWERPREP® II software directly from ETS’s website. It
contains two full-length adaptive revised General Tests. In addition, you can
download the PDF Practice Book for the Paper-based GRE® revised General
Test. While the format of the paper-based test is different from the computerbased test, the practice questions contained in the PDF are relevant and
useful.
ETS also publishes The Official Guide to the GRE® revised General Test.
This book can be found online or at most major book stores. Some of the
practice questions in that book, however, are identical to the questions in the
PDF, which is a free download.
Whatever you’re using, always practice with scratch paper. As you prepare
for the GRE, work through every question you do as if the question is being
presented on a computer screen. This means not writing anything on the
problems themselves. No crossing off answers, no circling, no underlining.
Copy everything to scratch paper and do your work there. You shouldn’t give
yourself a crutch in your preparation that you won’t have on the actual test.
About the Practice Tests in This Book
At the end of this book you’ll find two full-length practice tests. We
recommend that you download and print out the available PDFs of these
practice tests, which will allow you to fill in your answers using a pencil.
Please note that these paper-and-pencil tests do not adapt to your performance
like the real GRE. The actual GRE, as well as the online practice tests in your
Student Tools, are computer-adaptive; that is, the number of questions you
answer correctly on your first scored Math or Verbal section determines
whether you’ll get an easy, medium, or hard second section of that topic later
in the test. A paper-and-pencil test, of course, is not adaptive by section.
Scoring a paper-based test like the computer-adaptive GRE would require you
to stop and score each section during the test in order to determine the
difficulty level of your second section. But even this would not truly get you
closer to the computer-adaptive test experience, as you would be stopping to
calculate scores—which, of course, is not something that happens during the
real test. Much like the real exam, you won’t know the difficulty level of the
practice test questions. But you can still use the paper-and-pencil practice
tests in this book as opportunities to practice with the question types and
strategies, as well as work on your test-taking stamina.
Go Online!
Remember to check out
your Student Tools to gain
access to our computerbased practice tests for
the GRE. Follow the steps
on the Register Your Book
Online! page, which can
be found at the front
of this book.
MAKING A SCHEDULE
The GRE, like other standardized tests, is not a test for which you can cram.
While you may have fond memories from your college days of spending the
night before the midterm with a pot of coffee and a 500-page economics
textbook, that strategy won’t be as effective on the GRE. Why? Because, by
and large, the GRE is a test of patterns, not of facts. This book does its best to
reveal those patterns to you, but without sufficient time to practice and absorb
the information in this book, your GRE score is not likely to improve. Thus,
you should allow an adequate amount of time to fully prepare for the GRE.
You should allow yourself somewhere between 4 and 12 weeks to prepare for
the GRE. Obviously we can’t know exactly where you are in terms of your
starting score, your target score, and the amount of time you can devote to
studying, but in our experience, 4 weeks is about the minimum amount of
time you’d want to spend, while 12 weeks is about the maximum. There are a
number of reasons for these suggested preparation times. Attempting to
prepare in fewer than 4 weeks typically does not allow sufficient time to
master the techniques presented in this book. As you’ll see, some of our
approaches are counterintuitive and take some getting used to. Without
adequate practice time, you may not have full confidence in the techniques.
Additionally, vocabulary is part of the Verbal section of the GRE and it’s
difficult to substantially increase your vocabulary in a short period of time.
Finally, as mentioned before, the GRE contains a number of patterns, and the
more time you spend studying the test, the better you will be at recognizing
these patterns.
On the other hand, spending an inordinate amount of time preparing for the
GRE can have its downside as well. The first concern is a purely practical
one: There is a finite amount of GRE practice material available. Budgeting
six months of preparation time is unproductive because you’ll run out of
materials in less than half that time. Finally, spreading the material out over a
long period of time may result in your forgetting some of the lessons from the
beginning of your studies. It’s better to work assiduously and consistently
over a shorter time period than to dilute your efforts over a long time frame.
Premium Portal
You’re in luck! Since you
purchased the Premium
Edition, we have created
a few schedules for you
already! Go online to find
our 4-, 8-, and 12-week
GRE preparation schedules
and select the one
that is right for you.
STAY UP TO DATE
We at The Princeton Review will continue to learn all about the GRE as it
evolves. As you prepare for your GRE, make sure you periodically check
both our website at PrincetonReview.com and the GRE website at
www.ets.org/gre for the latest updates and information about the test.
WANT EVEN MORE PREP?
The Princeton Review offers an assortment of test preparation options:
Classroom and online courses plus private and small group tutoring. We also
have a bunch of other helpful GRE preparation books, including Math
Workout for the GRE, Verbal Workout for the GRE, 1,007 GRE Practice
Questions, and Crash Course for the GRE. When it comes to test preparation
for the GRE, we’ve got you covered.
Now that we have that introduction out of the way, let’s dive in and talk
strategy.
Even More GRE Titles!
For extra practice, check
out other GRE titles from
The Princeton Review.
Summary
The GRE is a 3-hour, 45-minute exam broken down into six sections
and used by graduate schools to rank applicants.
The GRE tests your mathematical, verbal, and writing abilities.
The importance of your GRE score varies from program to program.
Schools also consider your undergraduate record, your personal essays,
and your relevant experience.
GRE tests can be scheduled online at www.ets.org/gre.
Chapter 2
General Strategy
This chapter contains some basic advice to get you into The Princeton Review
mindset. You’ll learn some core test-taking strategies to help you maximize
your score. In addition, you’ll see some of the different question formats you
will probably encounter on test day.
CRACKING THE SYSTEM
Although ETS claims that the GRE measures “critical thinking, analytical
writing, verbal reasoning, and quantitative reasoning skills that have been
acquired over a long period of time,” that isn’t quite true. Again, what the
GRE really measures is how well you take the GRE. The first step to bettering
your GRE score is realizing that you can improve your score, in many cases
substantially, by familiarizing yourself with the test and by practicing the
techniques in this book.
I Thought the GRE Was Coach-Proof
ETS would have you believe that its tests are coach-proof, but that is simply
untrue. In many ways, taking a standardized test is a skill and, as with any
skill, you can become more proficient at it by both practicing and following
the advice of a good teacher. Think of your GRE preparation as if you were
practicing for a piano recital or a track meet; you wouldn’t show up at the
concert hall or track field without having put in hours of practice beforehand
(at least we hope you wouldn’t!). If you want to get a good score on the GRE,
you’ll have to put in the necessary preparation time.
Practice Your Way to
Perfection
The GRE is not a test of
intelligence. With practice,
you can conquer the GRE.
Why Should I Listen to The Princeton Review?
Quite simply, because we monitor the GRE. Our teaching methods were
developed through exhaustive analysis of all of the available GREs and
careful research into the methods by which standardized tests are constructed.
Our focus is on the basic concepts that will enable you to attack any problem,
strip it down to its essential components, and solve it in as little time as
possible.
Think Like the Test Writers
You might be surprised to learn that the GRE isn’t written by distinguished
professors, renowned scholars, or graduate school admissions officers. For the
most part, it’s written by ordinary ETS employees, sometimes with freelance
help from local graduate students. You have no reason to be intimidated.
As you become more familiar with the test, you will also develop a sense of
“the ETS mentality.” This is a predictable kind of thinking that influences
nearly every part of nearly every ETS exam. By learning to recognize the
ETS mentality, you’ll earn points even when you aren’t sure why an answer is
correct. You’ll inevitably do better on the test by learning to think like the
people who wrote it.
Cracking the System
“Cracking the system” is our phrase for getting inside the minds of the people
who write these tests. This emphasis on earning points rather than pinpointing
the correct answer may strike you as somewhat cynical, but it is crucial to
doing well on the GRE. After all, the GRE leaves you no room to make
explanations or justifications for your responses.
You’ll do better on the GRE by putting aside your feelings about real
education and surrendering yourself to the strange logic of the standardized
test.
COMPUTER-ADAPTIVE TEST
As discussed briefly in Chapter 1, the GRE is a computer-adaptive test, or
CAT for short. During the test, you will see two scored Math and Verbal
sections, and the difficulty of the second scored section of either subject is
determined by your performance on the first scored section. Depending on
your performance in the first scored section of a subject, you will receive an
easy, medium, or hard second section. Obviously enough, to achieve a high
score on the GRE you need to get as many questions correct as you can,
which means that the highest scores will result from performing well on the
first scored section and the hardest of the second sections. However, the
difficulty of an individual question plays no role in determining your score;
that is, your score is calculated by your performance on the entirety of the
scored sections, not just a handful of the hardest questions on a given section.
GENERAL STRATEGIES
1. Take the Easy Test First
Within a section, each question counts equally toward your score. There will
inevitably be questions you are great at and questions you don’t like. The
beauty of the GRE is that there is no need to bow to Phoenician numerical
hegemony; you can answer questions in any order you like. The question you
can nail in 25 seconds is worth just as much as the question that will torture
you for minutes on end. To maximize your score, leave the questions you
don’t like for last. If you are going to run out of time anywhere—and unless
you are shooting for a 160 or higher, you should be running out of time—
make sure that the questions that get chopped off are the ones you didn’t want
to answer anyway.
This strategy is called Take the Easy Test First. Skip early and skip often.
Doing so will result in two passes through an individual section. On the first
pass, cherry pick. Answer the questions you like. Get all of those easy points
in the bank before time starts running short. You know that the hard questions
—or the ones that you don’t like—are going to take more time. Also,
although you should never rush, everyone starts to feel the pressure of the
clock as time starts running low. This is often when mistakes happen. Leave
those difficult, time-consuming questions for the end of the test. If you run
out of time or make some mistakes at that point, it won’t matter because these
are low percentage questions for you anyway.
2. Mark and Return
On your first pass through the questions, if you see a question you don’t like,
a question that looks hard, or a question that looks time consuming, you’re
going to walk on by and leave it for the end. Sometimes, however, a question
that looks easy turns out to be more troublesome than you thought. The
question may be trickier than it first appeared, or you may have simply
misread it, and it seems hard only because you’re working with the wrong
information. From start to finish, the GRE is nearly a four-hour test. Over four
hours your brain is going to get tired. When that happens, misreading a
question is virtually inevitable. Once you read a problem wrong, however, it
is almost impossible to un-read the problem and see it right. As long as you
are still immersed in the problem, you could read it ten times in a row and you
will read it the same wrong way each time.
Whether a question is harder than it first appeared, or made harder by the fact
that you missed a key phrase or piece of information, the approach you’ve
taken is not working. This is where the Mark button comes in.
Reset your brain by walking away from the problem, but Mark the question
before you do. Do two or three other questions, and then return to the marked
problem. When you walk away, your brain doesn’t just forget the problem, it
keeps on processing in the background. The distraction of the other questions
helps your brain to consider the question from other angles. When you return
to the problem, you may find that the part that gave you so much trouble the
first time is now magically clear. If the problem continues to give you trouble,
walk away again.
Staying with a problem when you’re stuck burns time but yields no points.
You might spend change numerals to two, three, five, or even six minutes on
a problem but still be no closer to the answer. Spending five minutes to get
one point will not get you enough points on a 30- or 35-minute section. In the
five minutes you spend on a problem that you’ve misread, you could nail
three or four easier questions. When you return to the question that gave you
trouble, there is a good chance that you will spot your error, and the path to
the correct answer will become clear. If it doesn’t become clear, walk away
again. Any time you encounter resistance on the test, do not keep pushing;
bend like a reed and walk away. Use the Mark button to facilitate this key
skill. Skip early and often so that you always have questions to distract your
brain when you get stuck.
3. Use the Review Screen to Navigate
Within a single section you can mark an answered or unanswered question
and return to it later. In fact you can skip any question you like and return to
any question at any time you like. Navigating around a section is easy with
the new Review Screen, which looks like this:
Simply click on a question and hit the button marked “Go To Question,” and
you will return directly to that question. This opens up a whole new realm of
strategic opportunities for the savvy test taker.
4. There’s No Penalty For Guessing
You should take the easy test first and you should spend most of your time on
questions that you know how to answer, or are reasonably certain you can
answer.
You will be able to answer some of the questions that you mark and move on
from the second time around. A fresh set of eyes on a problem you’ve already
seen is sometimes all it takes for a solution to present itself. But there may
also be some questions that you do not know how to answer no matter how
many times you look at them.
When you confront a question like this, try to eliminate any answer choice
you can, but make sure to guess. There is no penalty for incorrect answers on
the GRE. As a result, its better to guess than it is to leave a question blank. At
least by guessing you stand a chance at getting lucky and guessing correctly.
5. Use Process of Elimination
Because there are many more wrong answers on the GRE than there are
credited answers, on some of the more difficult questions (those you do on
your second pass) you’ll actually be better served not by trying to find the
correct answer, but instead by finding the wrong answers and using POE,
Process of Elimination.
ETS Doesn’t Care How You Get the Correct
Answer
Remember when you were in high school, and even if you got a question
wrong on a test, your teacher gave you partial credit? For example, maybe
you used the right formula on a math question, but miscalculated and got the
wrong result, so your teacher gave you some credit because you understood
the concept.
Well, those days are over. There is no partial credit on the GRE. On the other
hand, ETS doesn’t know or care how you get the right answer. A lucky guess
is worth just as many points as a question that you solve completely and
correctly.
There is one thing for which we must thank ETS. They have actually given us
the answers! For most problems, there are five answer choices, and one of
them is correct. It is important to remember that the answer choices are part of
the problem. Many of them will be clearly wrong and can, therefore, be
eliminated. In fact, sometimes it is easier to identify the wrong answers and
eliminate them than it is to find the right ones. This approach is called Process
of Elimination, or POE.
POE will be crucial on the verbal side of the test. Vocabulary-based questions
will include plenty of words you don’t know. For such questions, you may not
be able to identify the correct answer, but you will certainly be able to
identify some wrong ones. Get rid of the wrong ones so that when you guess,
you have a fifty-fifty shot and not a 20 percent chance. The same holds true
for the reading comp questions, which will include plenty of answer choices
that are clearly wrong.
On the math side of the test, ETS loves to sucker you into doing more math
than is really necessary. You can often eliminate answer choices that are
clearly too large or too small. Sometimes it is even more efficient to eliminate
wrong answers than it is to do the math required to come up with the right
one.
The Importance of Distractors
By using POE, you will be able to improve your score on the GRE by looking
for wrong answers instead of right ones, on questions you find difficult. Why?
Because, once you’ve eliminated the wrong ones, picking the right one can be
a piece of cake.
Wrong answers on standardized multiple-choice tests are known in the testing
industry as “distractors,” or “trap answers.” They are called distractors
because their purpose is to distract test takers away from correct choices. Trap
answers are specifically designed to appeal to test takers. Oftentimes, they’re
the answers that seem to scream out “pick me!” as you work through a
question. However, these attractive answers are often incorrect.
Remembering this simple fact can be an enormous help to you as you sit
down to take the test. By learning to recognize distractors, you will greatly
improve your score.
Improve Your Odds Indirectly
Every time you’re able to eliminate an incorrect choice on a GRE question,
you improve your odds of finding the correct answer; the more incorrect
choices you eliminate, the better your odds.
For this reason, some of our test-taking strategies are aimed at helping you
arrive at ETS’s answer indirectly. Doing this will make you much more
successful at avoiding the traps laid in your path by the test writers. This is
because most of the traps are designed to catch unwary test takers who try to
approach the problems directly.
POE and Guessing
If you guessed blindly on a five-choice GRE problem, you would have a onein-five chance of picking ETS’s answer. Eliminate one incorrect choice, and
your chances improve to one in four. Eliminate three, and you have a fiftyfifty chance of earning points by guessing. Get the picture?
Guess, but guess
intelligently.
6. Use Your Scratch Paper
ETS doesn’t give you many useful tools on this test, so you have to make
good use of the ones they do give you. You will get six sheets of scratch paper
stapled into a booklet. You can get more by raising your hand during a
section, but that takes time, so you will need an efficient system for using
scratch paper.
Mistakes happen in your head, but good technique happens on scratch paper.
When you do work in your head, you are really doing two things at once. The
first is figuring out the answer at hand, and the second is keeping track of
where you’ve been. Mistakes happen when you try to do two things in your
head at once. It’s better to park your thinking on your scratch paper. Get it out
of your head and onto the page. Good things happen when you do.
Remember
By crossing out a clearly
incorrect choice, you
permanently eliminate it
from consideration.
On the math side, scratch paper is crucial. Not only is it important for
performing complicated calculations, but when used properly, it can actually
help to direct your thinking as you work through multi-step problems. In the
math sections of this book, we will give you graphic set-ups for each math
concept that you will encounter. Use them consistently, and they will become
good habits that will pay big dividends in accuracy, even over a four-hour
exam.
On the verbal side, scratch paper is every bit as essential. It will help you to
track your progress, to focus on only one answer choice at a time, and to work
through a series of answer choices efficiently. In the verbal section of this
book, we will give you a process for using scratch paper efficiently and
effectively.
7. Double-Check
Get into the habit of double-checking all of your answers before you click on
your answer choice—or answer choices. Make sure that you reread the
directions and have done everything they asked you to—don’t get the answer
wrong just because you chose only one answer for a question that required
you to choose two or more.
The only way to reliably avoid careless errors is to adopt habits that make
them less likely to occur. Always check to see that you’ve transcribed
information correctly to your scratch paper. Always read the problem at least
twice and note any important parts that you might forget later. Always check
your calculations. And always read the question one last time before selecting
your answer.
By training yourself to
avoid careless errors, you
will increase your score.
8. Let It Go
Every time you begin a new section, focus on that section and put the last
section you completed behind you. Don’t think about that pesky synonym
from an earlier section while a geometry question is on your screen. You can’t
go back, and besides, your impression of how you did on a section is probably
much worse than reality.
9. Don’t Make Any Last-Minute Lifestyle
Changes
The week before the test is not the time for any major life changes. This is
NOT the week to quit smoking, start smoking, quit drinking coffee, start
drinking coffee, start a relationship, end a relationship, or quit a job. Business
as usual, okay?
YOUR STARTING POINT
Before you dive in, you might wish to take one of the practice tests in this
book or online to get a sense of where you are starting out from. It can be a
good exercise to tackle a practice test before you know any strategies or have
reviewed any content—while you have relatively fresh eyes to the test-taking
experience. This will be a good initial impression and these first scores will
show you what content areas need your focus. Of course, you’ll review all
necessary content for the GRE (won’t you?), but this first test can serve as a
helpful guide. Then as you learn strategies and review math and verbal
content, you’ll have a genuine sense of accomplishment.
Now let’s get cracking!
Summary
You can increase your score on the GRE through practice and
successful application of test-taking strategies.
The GRE uses a variety of question formats throughout the test.
Not all questions on the GRE are of equal difficulty. Your Personal
Order of Difficulty should tell you which questions to spend time on
and which to skip.
Accuracy is better than speed. Slow down and focus on accumulating
as many points as possible. Forcing yourself to work faster results in
careless errors and lower scores.
Process of Elimination is an extremely useful tool on the test. Use it to
eliminate wrong answers and increase your odds of guessing correctly.
Part II
How to Crack the Verbal Section
3
The Geography of the Verbal Section
4
Text Completions
5
Sentence Equivalence
6
Reading Comprehension
7
Critical Reasoning
8
Vocabulary for the GRE
Chapter 3
The Geography of the Verbal
Section
The Verbal section of the GRE is designed to test your verbal reasoning
abilities. This chapter will review the types of questions you will see, how to
pace yourself, and the basic strategies that will best guide you through the
Verbal section. Additionally, this chapter will cover the importance of
vocabulary on the test, along with some useful tips on how to approach
learning GRE vocabulary.
WHAT’S ON THE VERBAL SECTION
ETS claims that the Verbal section of the GRE accomplishes the following:
•
places a greater emphasis on analytical skills and on understanding
vocabulary in context rather than in isolation
•
uses more text-based materials
•
contains a broader range of reading selections
•
tests skills that are more closely aligned with those used in
graduate school
•
expands the range of computer-enabled tasks
What does this mean for you?
•
There won’t be questions that involve analogies or antonyms on
this test, as there were on the old version of the GRE.
•
You’ll see some wacky-looking question formats that you’ve
probably never seen before.
•
Though they say the new version of the test de-emphasizes
vocabulary, there’s no getting around the fact that the more
vocabulary you know when you sit down to take the test, the better
off you’ll be. So vocabulary remains as important as it ever was. If
you’re especially eager to build your vocabulary, check out
Chapter 8: Vocabulary for the GRE.
There are three types of questions on the Verbal section of the test:
•
Text Completions
•
Sentence Equivalence
•
Reading Comprehension
Let’s take a brief look at each question type.
Text Completions
Text Completion questions consist of short sections of text with one or more
blanks; you are asked to choose the best word to place in each blank. You
may see one blank in the text, in which case you will be offered five answer
choices, or you may see two or three blanks, each of which will have three
answer choices. No partial credit is given for getting some but not all blanks
correct on a question, so be sure to read carefully.
Here is an example of a two-blank question:
Fables often endure due to their (i) ___________, often telling one simple
narrative, based around one character. This is both by design, because direct
statements are more easily remembered than florid ones, and by accident: As fables
are passed from teller to teller, (ii) ___________ details fall away, leaving only the
essential story.
Sentence Equivalence
This is another vocabulary-oriented question type. Each question will consist
of one sentence with six answer choices. Your job is to choose the two answer
choices that logically complete the sentence. As with Text Completions, there
is no partial credit, so you must select both correct answer choices to receive
points.
Here’s an example:
He was a man of few words, _______ around all but his closest friends.
laconic
garrulous
ascetic
taciturn
tempestuous
ambiguous
Reading Comprehension
Reading comprehension accounts for about half of the Verbal questions you
will see. Passages range from one to five paragraphs, and each passage can
consist of one to five questions. No matter the length, the passages offer some
type of argument that the author is trying defend, even if it’s just the author’s
opinion. Therefore, some of the questions in this section will ask you to
identify an author’s point of view or the assumptions and premises upon
which that point of view rests. Other Reading Comprehension questions will
ask about details of specific information in the passage or provable from the
passage, the structure or tone of the text, how a word is used in context, or the
main idea. Fortunately, these questions rarely test you on your prior
vocabulary knowledge. Furthermore, Reading Comprehension questions are
like an open book test—everything you need is right there in the passage!
You will encounter three Reading Comprehension question formats:
Multiple Choice
Select All That Apply
Select a Sentence
When you see a Select-a-Sentence question like the one above, you need to
click on the sentence in the passage that you think answers the question.
HOW IS THE GRE VERBAL SECTION
STRUCTURED?
The GRE has two scored multiple-choice verbal sections. Each will be
30 minutes long with 20 questions per section. The way you perform on one
Verbal section will affect the difficulty of the next Verbal section you are
given. Verbal sections tend to follow the same order. Roughly the first six
questions will be Text Completion, the next five or six will be Reading
Comprehension, followed by about four Sentence Equivalence questions, and
then another four or five Reading Comprehension questions. In profile, the
two verbal sections will look something like this:
A better performance on
the first scored verbal
section will yield more
difficult questions on the
second one!
BASIC STRATEGIES FOR THE GRE VERBAL
SECTION
Here are some strategies that will help you on the Verbal section. We’ll show
you how to use them as we go through specific question types in the chapters
ahead, but for now read through the strategies and get a sense of what they are
before moving on.
Accuracy vs. Speed
Any timed test will cause at least some level of stress. While it is important to
mark an answer to every question on the Verbal section, nobody has ever won
a medal for getting the most questions wrong in the shortest amount of time.
The key is to correctly answer the questions that you can get right. Be sure to
apply each step of the techniques that we will cover in upcoming chapters.
Don’t let that clock force you to make silly mistakes!
Mark and Move On
While it is important to be careful and process-driven when you take the
GRE, it is also important to allow yourself to see every question. After all,
question 20 could be the easiest one on the test for you.
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This is why the Mark button is important. If a question is not coming to you
immediately, it is not necessarily something that you cannot answer. On the
Reading Comprehension questions, for instance, you may struggle on a
question that deals with the main idea of the passage. You may even have
eliminated some answer choices. Don’t give up yet! If you have invested time
and work on a particular question, press the Mark button and move on. You
may find that after answering the next question, perhaps on specific content
from the passage, you have more insight and can return to the previously
marked question to answer it with ease.
There is also use for the Mark button on Text Completions and Sentence
Equivalences. Of course, some may have answer choices filled with
vocabulary that you have never seen before. In that case, you may just want to
guess and move on. On the other hand, you may be frustrated by a question
that has answer choices with which you are familiar. Mark that question and
move on. The time you could have spent staring at those answer choices
could be better used on another one or two easier questions. Coming back to
the earlier question with fresh eyes may help. If it doesn’t, simply guess on
that and other unanswered questions when there are two minutes remaining.
Bend—Don’t Push
Mark and Move is a crucial technique. Sometimes you just get stuck in a
mental rut, and continuing to stare at the same question is a waste of time.
Mark it, move on, do a couple other questions, and come back. You’ll be
surprised how often you’ll see something new just because you gave your
brain a break!
Over the course of a nearly four-hour test, your brain will get tired. When that
happens, you lose accuracy, make “silly” mistakes, and misread. Deal with
this inevitable pressure by allowing yourself to move on whenever the words
on the screen stop making sense. A fresh question can give you an
opportunity to regain your focus.
Need More Practice?
The Princeton Review’s
Verbal Workout for the
GRE, 6th Edition, includes
hundreds of drill questions
for the Verbal and Analytical
Writing sections.
Leave Nothing Blank
When you have two minutes left on a section, click the Review button and see
which questions are unanswered. Click through each of those unanswered
questions and pick something. You might be right, and there’s no penalty for
incorrect answers!
Process of Elimination (POE)
Determining correct answers on the Verbal sections of the GRE can be tricky.
Answer choices on Reading Comprehension questions, for example, are
constructed with “clever” wordings that make correct answers seem wrong
and incorrect answers seem right.
So, reverse your approach. Instead of looking for the correct answer,
eliminate the incorrect answer choices.
Using Process of Elimination (POE) will be the most effective way to avoid
trap answer choices.
•
Consider every answer choice, even if you think you know the
answer.
•
Eliminate any choice that contains something that you can point to
and say, “Well, I know that’s wrong.”
•
If a choice seems weird or confusing, or just doesn’t make sense
the first time you read it, leave it as an option.
•
Cycle through the answer choices until you’re down to one choice,
and then pick it.
Your first impression of POE might be to think that it would take way too
long, but don’t knock it until you try it. Then try it again, and again. Most of
the incorrect answer choices on the GRE Verbal sections can be quickly
identified by spotting some minor detail that can’t be supported. We’ll discuss
some of the ways to categorize these details in later chapters. For now, just
realize that POE can actually be faster than trying to find the “right” answer.
Before you pull out a stopwatch and time each method, realize that speed
matters a lot less than accuracy.
When you’ve eliminated four answer choices that you know are wrong,
you know that you’re left with the correct answer.
Down to Two?
The most common situation you’ll find yourself in is when you’ve eliminated
all but two answer choices and you can’t decide between them. Don’t just
pick one! Compare them and remind yourself what the answer to the question
should look like. There’s only one way to answer every question on the GRE,
so if you can’t see why one of the remaining choices is wrong, you are
missing something. Find it. If you’re really stuck, Mark and Move.
Stacking the Odds
Most likely, there will be some questions on the test that you know you won’t
be able to answer in time. POE can turn these questions into potential points.
Before you just guess on a question, quickly consider if some of the answer
choices are clearly wrong. If you can eliminate two choices on each of three
different questions, you’ve got a good chance of getting a free point!
Consider the following question:
When studying human history, one must be aware that the ____________ between
historical periods are arbitrary; certainly none of the people alive at the time were
aware of a shift from one era to another.
Here’s How to Crack It
If you encountered this question on the GRE, you might not know what the
best answer is (you’ll learn how to approach questions like this in Chapter 4).
However, you might see that some of the answer choices simply don’t make
sense. Choices (A), (B), and (C) don’t seem to fit the sentence at all. By
eliminating these wrong answers, you’ve suddenly given yourself a great
chance of choosing the correct answer just by guessing, since only (D) and
(E) are left. And if you realize that (E) doesn’t make sense either, then you
know the correct answer is (D), even if you’re not sure what demarcations
means.
POOD
Your Personal Order of Difficulty (POOD) should guide your approach to the
Verbal section. Do you have a lot of success on Reading Comprehension and
not much on vocabulary questions? Skip those six Text Completions for now
and work your strengths. You do not want to be put in a situation in which
you have to rush through the types of questions you would normally get
correct simply because they show up later in the section.
With this in mind, think of the Verbal section as two tests—one easy and one
difficult. Take the easy test first! Move briskly through the test, answering the
questions that give you little trouble and skipping the questions that will bog
you down. Do this all the way through question 20. Then go back and work
those harder questions knowing that you will not have missed any easy points
due to a lack of effective planning.
A Word on Vocabulary
While the GRE has scaled back on the sheer difficulty of vocabulary over the
years, you still need to have a grasp on the words that are commonly used on
the test if you want to see significant score improvements. In the coming
chapters, we will go over strategies for answering Text Completion and
Sentence Equivalence questions. However, there is no substitute for having a
good understanding of the vocabulary that ETS tends to test. In Chapter 8, we
offer the Key Terms List—a list of the most commonly used words tested on
the GRE.
Effective ways to study vocabulary for the GRE may include the following:
•
Prioritize words from the Key Terms List into three categories:
Words I Know, Words I Sort of Know, and Words I Do Not Know.
Spend most of your time studying the second group, followed by
the final group.
•
Read. You will absorb many of the words that will show up on the
GRE by reading respected publications such as academic journals
or some of the more highbrow newspapers and magazines.
•
Keep a vocabulary list. When you come across new words on
practice tests or practice problems, add them to your list. They
have been used before on the GRE and they may very well be used
again.
Stressed About Vocab?
Check out The Princeton
Review’s flashcards,
Essential GRE Vocabulary,
which includes 500
essential vocabulary
words plus 50
customizable cards!
Summary
The GRE Verbal section consists of two 30-minute sections, each
containing 20 questions.
The Verbal section is made up of Text Completions, Sentence
Equivalences, and Reading Comprehension.
Remember to utilize Process of Elimination (POE) to attack the wrong
answers.
Use your Personal Order of Difficulty (POOD) to ensure that you take
the easy test first. Skip questions that seem difficult, and Mark and
Move when questions get tough.
Vocabulary is important. Prioritize the words from the Key Terms List
into Words I Know, Words I Sort of Know, and Words I Do Not Know.
Chapter 4
Text Completions
If you took the SAT, you probably remember sentence completion questions.
Well, they’re back, retooled and renamed for the GRE. Text Completion
questions test your ability to figure out which word or words best complete a
given sentence or group of sentences. On the GRE, the sentence can have one,
two, or even three blanks that you must fill. This chapter will show you The
Princeton Review approach to Text Completions, a tried-and-true approach
that will help you focus on exactly the parts of the sentences that you’ll need
to figure out the answer. Along the way we’ll provide you with some valuable
tips on using Process of Elimination to help you when you don’t know all the
vocabulary on a question.
PART 1: TEXT COMPLETION BASICS
WHAT’S A TEXT COMPLETION?
On each Verbal section of the GRE you can expect to see about six Text
Completion questions, or approximately 30% of the total questions. Each
question is made up of a passage consisting of one or more sentences—
sometimes up to five! The passage has blanks in place of key words. There
can be one, two, or three blanks. One-blank questions have five answer
choices per blank, while two- and three-blank questions have three answer
choices per blank. Your job is to select the combination of answer choices—
one choice per blank—that best completes the text. The completed
sentence(s) must make sense as a whole. In multiple-blank questions, credit is
only given if all blanks are answered correctly.
Therefore, the correct choice for each blank depends on the meaning of the
sentence as a whole. While at first glance, Text Completions may seem to
focus on vocabulary, these questions are not just a glorified vocab quiz. Even
more important is a critical understanding of context and the ability to
recognize the internal logic of the passage. You cannot rely on word power
alone.
But you will need a strategy for approaching Text Completion questions. This
strategy is where we will begin our discussion of how to successfully navigate
Text Completions.
THE BASIC APPROACH FOR TEXT
COMPLETION QUESTIONS
Using the basic approach for Text Completion questions, you will examine
the sentence or sentences in the passage, which will include clues and
transition words that indicate the intended meaning of the sentence.
Examining these clues and transitions, you will aim to come up with your
own word for each blank to compare against the answer choices.
STEPS FOR TEXT COMPLETION QUESTIONS
Follow these steps for each blank in turn. For now, we’ll only be working
with one-blank questions. Later, we’ll tell you how to handle questions with
two and three blanks.
1. Find the clues and transition words. Ask yourself:
•
Who or what is the blank describing?
•
What else in the passage provides insight into that person or
thing?
2. Come up with your own word or phrase for the blank. Write
that word or phrase down on your scratch paper.
3. Check each answer choice.
an answer that sort of matches your word
an answer that does not at all match your word
? any word you don’t know
Before tackling the nuts and bolts of these steps, let’s try an example to get
started:
Robert Ingersoll, although virtually unknown today, was ____________ orator of
the nineteenth century; people traveled hundreds of miles to hear his eloquent
speeches.
Here’s How to Crack It
1. Find the clues and transition words. First ask, “Who or what is
the blank describing?” Before you try to fill the blank, you must
consider what the blank is talking about! In this sentence, the blank
describes the kind of orator that Robert Ingersoll was.
Next ask, “What else in the passage provides insight into that
person or thing?” Find information in the surrounding text that
provides insight into the kind of orator that Ingersoll was. The
sentence tells us that people traveled hundreds of miles to hear
his…speeches. So he was obviously a good orator. The sentence
also tells us that Ingersoll is virtually unknown today. The
transition word although puts this insight into opposition to the
word in the blank describing the kind of orator Ingersoll was. Now
you know that he wasn’t just a good orator but a well-known one.
2. Come up with your own word or phrase for the blank. Use the
insights you’ve gained to come up with your own word for the
blank. You don’t have to come up with the perfect word, and it
doesn’t have to be a single word. It’s better to be as literal as
possible in order to capture your insights. Feel free to recycle
language in the sentence when coming up with your own word.
From Step 1, you know that Ingersoll was a well-known orator—
recycled from the word unknown—and also a good one. To capture
all that, you could just call him “famously good.”
3. Check each answer choice. Only now that you’ve come up with
your own word (or phrase in this case) compare that word or phrase
to the answer choices. Compare each of the answer choices in turn
to your own phrase, “famously good.”
Choice (A) is domineering, which means bossy, is not a match for
“famously good.” Eliminate (A). Choice (B), eminent, is a famous
or respected person, so keep (B). The word unobjectionable, (C),
means something that can’t be objected to, so eliminate (C). Choice
(D), conventional, is practically the opposite of “famously good”,
so eliminate it. Choice (E), execrable, might stump you, in which
case you’d give it a question mark. Execrable means downright
detestable. If you knew that, you’d eliminate the word. Either way,
you’d go with the answer choice that you’ve assigned a checkmark,
(B). Ingersoll was an eminent orator of the nineteenth century.
Congratulations on completing your first Text Completion question!
GET A CLUE!
Here’s the good news about Text Completion questions: There is only ever
one answer choice that is correct. We know that seems obvious enough, but
it’s worth mentioning. It gives you a touch of insight into the reality of the
creation of Text Completion questions. Somewhere in the question, the
information to determine the correct answer is present. There are no
alternative interpretations or Mad-Lib style games for Text Completion
questions. The information to justify the answer is always right in front of
you.
The trick, as always, is to determine where and what that information is. Step
1 in approaching Text Completions is to find clues in the passage about the
word for the blank. The text of the passage provides the context for the correct
answer. Your mission is to determine the intended meaning of the passage,
based on the information in the passage. That’s why it’s very important to do
Step 1 first. Do not move on to Step 2 or look at the answer choices until
you’ve identified the clues in the sentence!
The clue is the information in the sentence that provides insight into the word
or phrase that goes in the blank. But before you can even look for clues, you
want a concrete idea of what exactly is missing. That’s why, when you start
on each Text Completion question, you need to find the clue. And, you begin
finding the clue by first asking yourself this question:
•
Who or what is the blank describing?
Take a moment to make sure you understand what’s being talked about by the
blank. If it’s not crystal-clear, then determine what part of speech the blank
should be. An adjective will be easiest to work with, because then the blank
merely describes the noun next to the blank. If it’s a verb that’s missing, the
blank describes some action or process. If it’s noun that’s missing, the blank
represents a person, thing, or idea—or often some aspect of another noun in
the passage. Once you know what the blank is describing, ask yourself this
question:
•
What else in the passage provides insight into that person or thing?
The next order of business is to find the information in the passage that tells
you something about the person or thing described by the blank. ETS never
gives you a passage where the word that belongs in the blank is subject to
opinion, debate, or poetic license. They always give you one or more pieces
of information that offer insight into the topic of the blank. This information
is the clue, and it’s all there in the text.
To illustrate the importance of the clue, let’s look at the following example:
Sophocles, who wrote the play Oedipus Rex, was one of the most _________
playwrights of ancient Greece.
Who or what does the blank describe? It’s an adjective describing the kind of
playwright Sophocles was. What else in the sentence gives you insight into
what kind of playwright Sophocles was? If you’ve come up empty-handed,
that’s because the sentence does not contain a clue. Based on what you may
know about Sophocles, a few of the answer choices may work. To answer this
question correctly, ETS would have to expect you to rely on outside
knowledge about Sophocles. For fear of an army of angry lawyers knocking
down their door, ETS will never produce a question that has a correct answer
they cannot defend. The clue has to be there in the text. Let’s try with another
version of the same question:
Sophocles, who wrote the play Oedipus Rex, was one of the most _________
playwrights of ancient Greece, completing 123 plays in his lifetime—double that
of any of his contemporaries.
Just as before, the blank should describe what kind of playwright Sophocles
was. This time, however, you’re given additional information: He completed
123 plays, which was double that of…his contemporaries. Now you have
something to work with in coming up with your own word. Sophocles wrote a
lot of plays, so “productive” could be your word. You could even put down
“adjective—wrote lots” on your scratch paper if you weren’t able to come up
with a single word that means “wrote lots.” Remember that your job is to
simply come up with a word or phrase that leads you to the correct answer.
So, it’s okay if your word is actually a phrase.
Now you’re ready to take on the answer choices. The adjective famous is
certainly tempting. Sophocles was unquestionably one of the most famous
playwrights of ancient Greece. But this has no connection to the clue, which
is all about the number of plays he wrote. This is a trap laid by ETS writers.
ETS writers may not be able to use outside knowledge to create their correct
answer choices, but they certainly can add in an incorrect answer choice
relying on outside knowledge and hope the student does the rest. Assumptions
and extrapolations are dangerous. One and only one of the answer choices
matches the clue—(D), prolific. The other four words may indeed describe
Sophocles and sound fine if inserted into the sentence. But only one answer
choice will ever match the clue, and that’s what counts.
A WORD ABOUT YOUR WORDS
Once you’ve found the clue in the passage, you’ve done most of the heavy
lifting. Now it’s time to come up with your own word to go in the blank. This
is Step 2 of the basic approach.
This isn’t about predicting the answer. You’re just trying to come up with
something that reflects the clues and will help you to identify the correct
answer from among the choices. So don’t waste time brainstorming the
perfect GRE word to put in the blank. Think of your job as supplying the
definition of what should go in the blank. To make your life easier, recycle!
Just use a word or phrase recycled from the clues. What better way to capture
the information you gleaned from the passage?
Practice: Finding the Clue
Underline the clue in each of the following sentences. Then, think of your
own word for the blank and write it down. Answers can be found in Part V.
Be systematic! Ask
yourself these questions.
Who or what is the blank
describing? What in the
sentence gives insight
into that?
1 of 8
The ____________ relationships in his life haunted Eugene O’Neill and are often reflected in the
harrowing nature of many of his plays.
2 of 8
Mount Godwin-Austen, more commonly known as K2, is the second highest mountain in the world,
with its ____________ peaks reaching more than 28,000 feet high.
3 of 8
A wind-chill warning is issued when the temperature is projected to reach minus 25 degrees Fahrenheit
or lower, the point at which the cold has ____________ effects on living creatures.
4 of 8
Divers still stumble across unexploded shells, 70-year-old ____________ from World War II, in the
waters outside Tokyo.
5 of 8
Although some people use the terms interchangeably, mastodons and mammoths were quite
____________; mammoths were hairy with long tusks, while mastodons had low-slung bodies and
flatter skulls.
6 of 8
The mayor was definitely ____________; he crafted his policies not with an eye toward their political
consequences but instead toward their practical effects.
7 of 8
The first-year law student was amazed at the sheer ____________ of the material he had to read for his
classes; he imagined that he would have to read for hours and hours each day to finish it all.
8 of 8
Our word “ghoul” is ____________ from the Arabic word “Algol,” the name for the Demon Star, a star
in the constellation Perseus.
NEXT, TRANSITIONS
Let’s take another look at the mastodon/mammoth question from the
preceding Finding the Clue practice exercise:
Although some people use the terms interchangeably, mastodons and mammoths
were quite ____________; mammoths were hairy with long tusks, while
mastodons had low-slung bodies and flatter skulls.
The first phrase of the sentence says that some people use the terms mastodon
and mammoth interchangeably. However, the clause after the semicolon
describes each animal, making it plain that they are very different in
appearance. The clue to the word that goes in the blank is the word
interchangeably, but context indicates that the word for the blank is the
opposite of the clue. The reason you know this is because the phrase
containing the clue begins with the transition word [a]lthough.
Transition words tell the reader how a clue relates to the blank—whether the
clue has the same meaning as the blank or the opposite meaning. Consider the
following two scenarios:
I won the lottery, and…
I won the lottery, but…
The first sentence is going to have a happy ending. The second one, not so
much. Changing a single word sets up dramatically different outcomes. The
same scenarios could also have been written with different transition words
placed at the beginning:
Because I won the lottery,…
Although I won the lottery,…
Some transition words simply reinforce the clue. For these, you’d pick a word
that agrees with the clue. Other transition words indicate that the word for the
blank is the opposite of the clue. It’s particularly important to take note of
these contrast transitions.
Here are some of the most important transition words you’ll encounter in Text
Completion questions:
Two of the same-direction transition “words” are just punctuation marks. The
semicolon is the equivalent of and, implying that the second clause follows
logically from the first. The colon implies that the second clause is an
explanation or illustration of the first. In either case, the clue for a blank in
one part of the sentence will be found in the other part. Notice nuances in
some of these transition words. Several of the same-direction words imply a
cause-effect relationship: accordingly, because, consequently, hence, so,
therefore, and thus. The word previously implies a change or contrast over
time, and the word unfortunately implies a situation contrary to what was
hoped for or expected.
Practice: Clues and Transitions
Underline the clues and circle the transition words in the following sentences;
then come up with your own word for the blanks. Recycle the clues if
possible. Answers can be found in Part V.
1 of 8
The star receiver is widely regarded as one of the top talents in the game, but his ____________
performance as a rookie almost ended his career.
2 of 8
The prime minister received international ____________ for her work; she brokered a diplomatic
solution to a potential crisis.
3 of 8
While it is often assumed that drinking alcohol is detrimental to one’s health, many studies have shown
the ____________ effects of having a glass or two of wine daily.
4 of 8
Despite the increasing technological connectivity of the modern world, many cultures still remain
____________ from the global society.
5 of 8
Although many cultures view the toad as a symbol of ugliness and clumsiness, the Chinese revere the
toad as a ____________ symbol.
6 of 8
Stock analysts often use holiday sales to gauge future stock prices; thus, retail performance can be an
important ____________ of market trends.
7 of 8
It is somewhat ironic that while the population at large tends to have a negative view of the legal
profession, individuals rarely display such ____________ to their lawyers.
8 of 8
Methyl bromide is a pesticide that has devastating effects on insects; however, some believe it has the
same ____________ to humans.
PROCESS OF ELIMINATION STRATEGIES
After deciphering the clues in the passage and coming up with your own word
for the blank, you arrive at the third and final step in Text Completion. In Step
3, you simply check each answer choice against the word you came up with.
Use your scratch paper to mark any choice that’s a match for your word with
a , any choice that’s not a match with a , and any word you don’t know
with a ?.
Ideally, your scratch paper will show one , five s, and no ?s. But life’s not
always that simple, and neither is the GRE. For those less-than-ideal
situations, you’ll need some POE skills and strategies to fall back on.
Here are some general points to keep in mind as you work through the answer
choices.
•
Focus on the words you know. Any answer choice that you
know, you should be able to compare to your word and decisively
mark with a or a .
•
Never talk yourself into picking a word that you’ve eliminated.
Just because you know what it means does not mean the word is a
better answer. If you are between choosing a word you’ve
eliminated and choosing a word you don’t know, pick the word
you don’t know.
•
Never eliminate a word you don’t know. If you have no good
idea what an answer choice means, you can’t rule it out as a match
for your word.
•
Don’t trust your ears. If an answer choice matches your own
word but doesn’t sound quite right when inserted into the blank, it
may still be correct. The question may be relying on a less
common definition or usage of the word. Sometimes, too, the GRE
will create a correct answer choice that’s somewhat awkward
while planting a trap answer that sounds better to the ear but has
nothing to do with the clues.
•
Don’t forget to Mark and Move. There are certain situations
where Mark and Move makes sense on Text Completion
questions. You might be having difficulty finding the clues. You
might be daunted by a multi-blank question. The definition of a
familiar word may have momentarily slipped your mind. You
might have gone through POE and have two answer choices with
checkmarks. In such cases, step away from the question, answer a
few other questions and return to the one you’ve skipped. It’s the
best way to reset your brain and get a fresh start on a difficult
question.
Take a look at the following example:
Years of confinement in a sunless cell had left the prisoner wan and weakened,
with a shockingly ____________ appearance.
Here’s How to Crack It
Begin by asking “Who or what is the blank describing?” The blank is
describing the prisoner’s…appearance. Now ask “What else in the passage
provides insight into the prisoner’s appearance? The sentence describes this as
wan and weakened. Therefore, recycle the words “wan and weakened” as the
word for the blank. Now evaluate the answer choices one at a time.
Upon evaluating the answer choices, many will find that they are a total
nightmare. Resolutely work through the answer choices one by one,
comparing them to “wan and weakened.” Choice (A) is tough. If you don’t
know this word, you can’t eliminate it, so mark with a question mark and
leave it for now. You may know that (B), boisterous, means noisy and rowdy.
If so, you can eliminate (B). The next choice, (C), is etiolated—another
difficult word, so mark it with a question mark and move on. Choice (D) is
singular, which we usually think of as the opposite of plural. It can also mean
one-of-a-kind or unique. In either sense, it’s not a match for “wan and
weakened,” so eliminate (D). The final choice, (E), is circumscribed, which
means to restrict something, or draw around, so eliminate (E).
At this point, you have three eliminated choices and two with question marks,
so pick one of the two unknowns. The bottom line is that by using careful
POE you have increased your odds to one-in-two. By the way, the answer is
(C), etiolated, which describes the pale appearance of plants grown with
insufficient sunlight but by extension applies to anything feeble or sickly in
appearance.
Positive and Negative Words
In some cases, your search for the clues will be less than conclusive. You
might find the clues vague. You might be uncertain about the precise meaning
of the word to go in the blank. Or, you may be faced with an intimidating
lineup of answer choices. In situations such as these, try to simplify your
POE. If you can determine whether the general sense of the word to go in the
blank is positive or negative, you can separate the answer choices
accordingly.
Look again at question 3 from the Finding the Clue practice exercise:
A wind-chill warning is issued when the temperature is projected to reach minus 25
degrees Fahrenheit or lower, the point at which the cold has ____________ effects
on living creatures.
You might not be able to think of a good word to fit in the blank, but common
sense (plus the clue that a warning is issued) tells you that temperatures of
minus 25 degrees…or lower are bad for living creatures. So you can eliminate
any answer choice that implies positive or beneficial—or even neutral!—
effects on living creatures. This approach may not eliminate every answer
choice (it may not eliminate any!), but every little bit helps. With a little
thought, you might be able to take this positive/negative aspect of the passage
a step further and eliminate any answer choice that doesn’t reflect negative
influences on health specifically.
It’s important to remember that this strategy must not be your main approach
to Text Completion questions. Your surest path to success remains the basic
approach of finding clues and coming up with your own word to check the
answer choices against. Positive/negative word associations can help you to
leverage your vocabulary up to a point but should remain a tool of last resort.
THE FINAL WORD ON VOCABULARY
The strategies that we’ve been discussing emphasize critical assessment of the
passage and smart POE. They’re designed to make Text Completion questions
as easy as possible and will get you far. Learning these strategies will also
make you a better test-taker overall.
But there’s no getting around it. At the end of the day, Text Completions are
about knowing words and their definitions. These questions are about
vocabulary. You’ll see this most clearly (and painfully) on the questions
where you successfully come up with a great word for the blank only to hit a
slate of unfamiliar answer choices. Or the passage itself may be a minefield of
verbiage, making it all but impossible to decipher the clues. The only solution
for this predicament is to improve your vocabulary as much as possible, little
by little, from now until test day.
Memorizing the Key Terms List of words in Chapter 8 is a good start. Try out
the suggestions for Learning New Words at the beginning of that chapter.
Deepen your vocabulary by exploring word roots as highlighted on this page
of the Sentence Equivalence chapter. Bottom line: As you prepare for the
GRE, keep learning new words every day, in whatever way works best for
you. Make it fun!
PUTTING IT ALL TOGETHER
The following drill is your opportunity to apply all the skills and strategies
you’ve learned so far. These are all one-blank Text Completion questions,
each with five answer choices.
Remember how to go about it! Start by assessing the text to come up with
your own word for the blank. Ignore the answer choices. Ask who or what the
blank is describing—identifying the part of speech can clarify this. Then ask
what else in the sentence gives insight into this person or thing. These are
your clues, and you’ll use transition words to determine whether the clues
have the same or opposite meaning relative to the blank. Now, come up with a
word or phrase for the blank. Use plain, descriptive, and literal language,
recycling words from the clues if possible.
Compare each answer choice to your own word—eliminating words that
don’t match ( ), keeping the word that does ( ), and leaving any words you
don’t know (?). If it’s not that straightforward, use your POE tools. Bear in
mind that some words have figurative or uncommon usages that may sound
awkward even if they are close to your own word and match the clues. If
guessing, never choose a word you’ve eliminated over one you don’t know.
Use the positive-and-negative approach to POE only if your understanding of
the clues is vague or you’re stumped by the majority of answer choices. If you
wind up with two answer choices that work or find yourself paralyzed by a
question for any other reason, use Mark and Move.
Good luck!
Text Completions Drill
Answers can be found in Part V.
1 of 6
Despite the smile that spread from ear to ear, her eyes relayed a certain ____________ .
2 of 6
While grizzly bears have long, flat, and somewhat blunt claws, black bears have short, curved and
____________ claws.
3 of 6
One of social science’s major themes is that of stability versus change; to what extent are individual
personalities ____________ or different over time?
4 of 6
The Erie Canal’s completion caused _________ economic ripples; property values and industrial output
along its route rose exponentially.
5 of 6
Voters have become so inured to the fickle nature of politicians that they responded to the levy of a new
tax with ____________ .
6 of 6
It is desirable to expand the yield of a harvest only when ____________ additions in time, exertion, and
other variable factors of production are not also required.
PART 2: TEXT COMPLETION ADVANCED
TOPICS
So far we have been dealing with one-sentence, one-blank Text Completions
with five answer choices. But not all Text Completion questions are created
equal. Some are designed to be more challenging, but ETS has a specific
repertoire of techniques it uses to make hard Text Completion questions.
While it’s true you will never see the same question twice, ETS does
repeatedly pull from the same bag of tricks to make questions harder. No
matter how tricky a question looks, however, the ground rules remain the
same: The text contains the clues that tell you what goes in the blank(s).
Let’s take a quick look at how ETS mixes things up in advanced Text
Completion questions:
•
More Blanks. Some passages have questions with two or three
blanks. In such questions, each blank has three answer choices, not
five as in one-blank questions.
•
More Sentences. Text Completion questions don’t all have just a
single sentence. Some are passages of up to five sentences. That
means more to read and more to keep track of, but also more
information about the blanks.
•
More Complicated Sentences. ETS will make the structure of the
sentence more difficult to read. They will make the language
thicker and harder to follow.
•
Difficult Transitions. Transitions—agreement or contrast between
parts of a passage—may not always be marked by obvious words
like and, but, since, and although. And some sentences contain
multiple transitions.
•
Vocabulary. The words in the answer choices may be more
difficult. However, it’s more typical for ETS to make harder Text
Completion questions by including more challenging vocabulary
in the passage itself.
STEPS FOR TWO- AND THREE- BLANK TEXT
COMPLETIONS
For two- and three- blank text completion questions, there are only three
answer choices per blank. With just three answer choices per blank, multipleblank questions have a simpler POE per blank than one blank Text
Completions. But that makes it even more important to analyze the text for
clues about the word that goes in the blank. The strategies you’ve already
learned in this chapter still apply, no matter how involved the question, but
multiple blanks call for some slight modifications to the steps:
•
Start with the easiest blank. This is not always the first blank.
The easiest blank is the one with the most obvious clue. Read
through the passage and determine the blank that has the most
obvious clue and begin working there.
•
Answer each blank in turn. Once you identify the blank with the
strongest clue, work through the POE process for it first before
moving on to another blank.
•
Reread the finished product. Once you have selected answer
choices for all the blanks, reread the entire passage with your
choices. Make sure that it tells a consistent, logical story—the only
possible story given the context of the passage.
Let’s apply this modified approach to the following example:
Federal efforts to regulate standards on educational achievements have been met by
(i) ____________from the states; local governments feel that government
imposition represents an undue infringement on their (ii) ____________.
Here’s How to Crack It
Without looking at any answer choices yet, scan the passage and determine
which of the blanks has the more obvious clue. Because the second clause
makes it clear that something bad is going on—an undue infringement, the
first blank is easier to work with. The first blank is describing the states’
reaction to [f]ederal…standards on education achievements. The sentence
gives further insight into this by stating that local governments consider this
an…infringement. The semicolon is a transition indicating agreement between
the clauses. So, the word in the first blank describing the states’ reaction will
be something like “resistance.” Now check the answer choices against
“resistance.” Choice (A) is the opposite of this, receptivity. Eliminate (A). If
you don’t know what intransigence means, then put a question mark next to
(B). Choice (C), however, compromise, is not a match for “resistance.” Even
if you don’t know what intransigence means, select (B) as it is the only noneliminated answer. Now, work with the second blank.
The second blank describes something that local governments feel is
negatively impacted by government imposition. The sentence provides insight
into this by stating that [f]ederal efforts to regulate standards on education
achievements, have not been well-received by the states. A word or phrase for
the second blank, then, could be a descriptive phrase like “freedom from
intervention by the federal government,” which you might simplify to “the
right to govern themselves.” Now check the answer choices. Choice (D),
autonomy, means independence or self-government. This is a good match, so
keep (D). Choice (E), legislation, is close but too neutral and broad given the
clue. Eliminate (E). Choice (F), comportment, means demeanor or the way
one carries oneself, so eliminate it.
The correct answer is intransigence and autonomy.
Let’s try our hand at a three-blank question:
Many popular musicians have (i) ____________ new digital technologies that
allow them unprecedented control over their music. These musicians use
computers to (ii) ____________ and modify their songs, resulting in a level of
musical precision often unattainable naturally. Of course, though, as is often the
case with new technologies, some traditionalists (iii) ____________these
developments.
Here’s How to Crack It
The second blank has the strongest clue, so begin there. The second blank is a
verb that describes what musicians do to their songs using computers. The
sentence gives further insight into how musicians use computers to impact
songs by stating that computers result in a precision…unattainable naturally.
The transition word and indicates that the word for the blank should be
similar to the word modify, which the passage uses to describe the contents of
the blank. So, recycle this language and use a word such as “modify.” Choice
(D), energize, is not a match for “modify,” so eliminate it. Choice (E),
delineate, means to outline or to define, which is also not a match for
“modify,” so eliminate (E). Although both these words describe something
that musicians could do to their songs, neither is as close a match for the word
“modify” as (F), recast. Keep (F) and move on to the blank with the next
strongest clue.
The blank with the next strongest clue is the first blank. The first blank should
be a verb describing what [m]any popular musicians have done with new
digital technologies. The passage gives further insight into what musicians
have done with new technologies by stating technologies gives them control
over their music and that [t]hese musicians use computers. Therefore, the
word for the first blank should be something close to “use,” so let’s reuse that
fairly neutral word. The word for (A), incorporated, is a good fit, so keep (A).
Choice (B), synthesize, is a trap answer. It may describe how musicians make
their songs using digital technologies, but it doesn’t describe what they do to
these technologies. Eliminate (B). Choice (C), alleviate, means to make less
severe, so also eliminate (C).
Now work with the third blank. The third blank is a verb describing the
reaction of traditionalists to these developments. The passage provides further
insight by stating that these are new technologies and the transition word
though indicates that the reaction from traditionalist should be expected to be
different than those of the musicians described earlier. Therefore, the
traditionalists should have a negative reaction to new technologies, so a good
phrase for the blank could simply be “don’t like.” Choice (G) is balk at,
which matches “don’t like,” so keep (G). Choice (H), revel in, means
celebrate, which is the opposite of “don’t like,” so eliminate (H). Choice (I) is
retaliate, certainly negative but this extreme reaction is not suggested by the
text, so eliminate (I).
The correct answer is incorporated, recast, and balk at.
RELATIONSHIP BETWEEN THE BLANKS
Sometimes, there is no clear clue for the blank. On occasion (maybe once per
test), there is no clear clue because the blanks are related to each other. If
you’re struggling to find a clear clue for either blank, look for how the
transition words connect the two blanks. If you find a transition word that
connects the two blanks, come up with a pair of words that work for the
blanks. Or, all you may be able to determine is that the two words go in the
same or opposite directions.
Once you have a pair of words that work for the blanks, work through the
choices for the first blank. When you find a word that works with your word,
put a checkmark next to it and begin evaluating the words for the second
blank. If you find a word in the answers that works for the second blank that
also pairs well with the first blank, put a check next to it. Continue that
process until you have gone through all of the potential answer choices for the
first blank. If you end up with more than one pair of words that work for the
blanks, re-evaluate the sentence and work those blanks again.
Oftentimes, students will be scared off of their game by questions like this
with no clear clue. The good news is these types of questions are relatively
rare. Just stick to the process and keep your cool. But because these questions
only show up on average once per test, you can always make a guess and
devote your time to more customary questions.
TRICKY TRANSITIONS
Transitions indicate that two parts of the sentence are the same or opposite,
similar or different, agreeing or contrasting. Not every transition is flagged by
the obvious transition words that we highlighted in the earlier section: and,
but, so, however, because, despite, since, although, instead, etc. Let’s take a
look at examples of more elusive transitions:
They were twins in ______________ only: their personalities
could not have been more ______________.
The word twins indicates that similarity is expected. The word only, however,
suggests that their similarity is limited to one aspect, because (note the
transitional colon) another aspect, their personalities, was not twin-like. The
word in the first blank should match “appearance”; the word in the second
blank should match “different.”
Here the similarity was implied by the word twins. Similarity or difference
could be implied by a mere description of two things:
Among dog breeds, the endearingly diminutive shihtzu has
____________ close kinship to its lupine ancestors.
The word close kinship implies similarity between the…shihtzu and the wolf
(lupine ancestors). However, the description of the shihtzu as endearingly
diminutive contradicts our typical image of the wolf. Therefore, the word in
the blank describing the close kinship between the two would be something
like “(an) unexpectedly”.
Suffice it to say there are many ways to set up agreement or contrast between
two parts of a sentence. The GRE will often use time transitions to indicate
some sort of change or difference. The GRE will also unfurl words such as
unexpected, surprising, ironic, or unfortunate. These words imply opposition
or contrast to what was expected or hoped for. Things really get complicated
when a sentence contains more than one transition. Read the following
example and its variations:
1. It’s ironic that the striking nurses’ chief grievance is ____________
health care.
2. It’s ironic that, while content with their salaries and vacation
packages, the striking nurses’ chief grievance is ____________
health care.
3. It’s ironic that, while pressing for better salaries and vacation
packages, the striking nurses’ chief grievance is ____________
health care.
4. It’s ironic that, while content with their salaries and vacation
packages, the striking nurses’ chief objective is ____________
health care.
In the first sentence, the word ironic indicates opposition between two things
in the sentence, the striking nurses and their chief grievance or complaint.
This complaint has to do with the kind of health care they are receiving.
Since nurses work in the health care field, it would be ironic for them to have
“poor” or “inadequate” health care, so that should be their complaint. The
second and third sentences are the same except for two very different
transitional clauses: the clause in the second sentence implying that the nurses
are happy with their salaries and vacation packages, the clause in the third
sentence implying that they are not. Even though these transitional clauses
have opposite meanings, they have no impact on the word in the blank. In all
three sentences, the word in the blank is driven by the ironic opposition of
striking nurses and their complaint of “inadequate” health care. In the fourth
sentence, we replace the word grievance in sentence 2 with objective. While
the irony of the nurses and their inadequate health care remains the same,
changing grievance to objective means that the word in the blank must change
from the kind of health care the nurses are complaining about (“inadequate”)
to the kind of health care they are aiming for (“better”).
Including multiple transitions in a passage is a predictable trick that ETS uses
to complicate Text Completion questions. So get used to recognizing and
deciphering them! It’s impossible to establish set rules for how these
compound transitions add up. You must pay close attention to how they are
related logically.
Text Completions Practice Set
Answers can be found in Part V.
1 of 10
With global interconnectedness on the rise, the conviction of the United States to remain neutral in
World War I seemed ever more ____________ .
2 of 10
Upon visiting the Middle East in 1850, Gustave Flaubert was so ____________ belly dancing that he
wrote, in a letter to his mother, that the dancers alone made his trip worthwhile.
3 of 10
The human race is a very (i)____________ species, as the facade of calm that covers our anxiety and
(ii) ____________ is flimsy and effortlessly ruptured.
4 of 10
The practice of purchasing books was primarily a (i)____________ of the well-to-do until the late
1800s, when the increased popularity of dime novels, the expansion in the number of bookstores, and
the introduction of the paperback made books (ii)____________ the average man.
5 of 10
Increasingly, the boundaries of congressional seats are drawn in order to protect incumbents, as
legislators engineer the demographics of each district such that those already in office can coast to
(i)____________ victory. Of course, there is always the possibility that the incumbent will face a
challenge from within his or her own party. Nevertheless, once the primary is over, the general election
is (ii)____________ .
6 of 10
While more (i)____________ professors continue to insist that video games will never be a proper
object of study, the rising generation of more heterodox academics is inclined to view such talk as
positively (ii)____________ .
7 of 10
Political predictions generally prove fairly accurate when the presumption that the future will be similar
to the past is (i)____________ . In periods with substantial (ii)____________ in the political world,
however, predictions can be (iii)____________ wrong.
8 of 10
Water is one of the few molecules that is less (i)_____________ as a solid than as a (ii)____________;
if you need (iii)____________, just look at the floating ice in your water glass.
9 of 10
As Molly was (i)____________ Spanish with her friends before their trip to Chile, she discovered that
although she could comprehend her friends, she could not (ii)_____________ her thoughts in the
(iii)____________ language.
10 of 10
People accustomed to thinking that the human lifespan (i)____________ the outer bounds of animal
longevity tend to dismiss tales of musket balls being found in the shells of living turtles. Samantha
Romney, however, argues that while such stories may be (ii)____________, some turtles do indeed
exhibit a phenomenon known as “negligible (iii)____________,” showing no signs of aging even as
they pass the two-century mark.
Summary
In Text Completion questions, ignore the answer choices and come up
with your own word for the blank(s), using the clues and transition
words in the passage.
To find the clue, ask these questions: “Who or what is the blank
describing” and “What else in the passage gives insight into that?”
Transition words tell you whether the word in the blank should have the
same sense as the clue or the opposite sense. Transitions are often
marked by obvious words like and, but, so, however, because, despite,
since, although, instead, etc.
When coming up with your own word for the blank, be as literal as
possible. It’s okay to use simple words, a descriptive phrase, or
language recycled from the clue.
After coming up with your own word for the blank, use POE to
eliminate words that aren’t matches for your word. Focus on the words
you know. Never eliminate a word that you don’t know.
If the clue is hard to decipher, you can simplify POE by determining if
the word to go in the blank should be positive or negative. Then narrow
down the answer choices by eliminating those that don’t match.
If the sentence has two or three blanks, do the blanks one at a time. Pick
the easiest blank to start with, ask the questions, find the clue, come up
with a word, and use POE. Then repeat for the remaining blanks. When
done, plug in all answer choices to double-check the meaning of the
passage.
Harder questions may have less obvious transitions or more than one
transition. Look out for anything that sets up a similarity or difference
between two elements of the sentence—things, ideas, actions, etc. Pay
attention to how transitions are related and the overall logic of the
passage.
Use Mark and Move if you need a fresh start on a question. Answer a
few other questions and then come back to the marked question.
Keep working on vocabulary every day! Learn prefixes, suffixes, and
other word roots. Learn not just the main definition of a new word but
the secondary and figurative meanings.
Chapter 5
Sentence Equivalence
This chapter details a variation on the Text Completions you learned about in
the prior chapter. Sentence Equivalence questions require you to find the best
word to complete a sentence. For these questions, however, you’ll have to
pick the two answers that best complete the sentence; this means the two
correct answers will be synonyms. Because both words create sentences that
are equivalent—both have the same meaning—we refer to these types of
questions as Sentence Equivalence questions. This chapter shows you how to
apply the strategies you learned last chapter and use Process of Elimination to
answer these questions.
WHAT’S A SENTENCE EQUIVALENCE?
Sentence Equivalence questions make up approximately 20% of the questions
in any individual Verbal section. There are usually four Sentence Equivalence
questions in each Verbal section. These questions are similar to Text
Completion questions, as both require test-takers to select the answer choices
that best complete the intended meaning of the given sentence. However,
unlike Text Completion questions, Sentence Equivalence questions always
have only one blank and six answer choices, and you will need to correctly
select two answer choices to get credit for the question.
Sentence Equivalence questions look like this:
Anthropologists contend that the ancient Mesopotamians switched from grain
production to barley after excessive irrigation and salt accumulation made the soil
___________ grains.
indifferent to
inhospitable to
unsuitable for
acrimonious to
benignant to
inured to
The goal of a Sentence Equivalence question is to choose the two answer
choices that complete the sentence, fit the meaning of the sentence as a whole,
and produce completed sentences that are alike in meaning.
A CAUTIONARY TALE ON SYNONYMS
A common mistake that test-takers make is expecting answer choices that
produce completed sentences that are alike in meaning to be synonyms. The
test-taker making this mistake believes when two synonyms are present in the
answer choices, they must be the correct answer. The test writers know this is
a commonly made assumption, so they use this information to trick test-takers
into selecting the wrong answer choices. But this question type is called
Sentence Equivalence, not Word Equivalence!
The first way they trick test-takers is by including a pair of synonyms in the
answer choices that do not fit the meaning of the sentence as a whole. They
are expecting a certain number of test-takers to scan the answer choices, find
two answer choices that are synonyms, and select them as their answer. These
test-takers will be sad to find that they have just been tricked by the test
writers.
The second way the GRE writers trick test-takers is by ensuring that the two
correct answer choices are not synonyms at all. The correct choices for
Sentence Equivalence questions do not need to be exact synonyms, as long as
both words correspond to the clues and the meaning of the sentence remains
consistent with both words.
Sometimes, the test writers combine these two tricks and include as answer
choices synonyms that are incorrect and correct answer choices that are not
synonyms.
Let’s look at an example:
Unconventional political ideology is considered ____________ existing main
stream political ideology until the new ideas gather enough evidence and support to
be adopted by or replace existing ideologies.
in juxtaposition to
inconsequential to
deviant from
a threat to
in light of
foreboding to
The correct answer is (B) and (C), even though inconsequential to and deviant
from are not even near-synonyms. Don’t worry too much yet about the best
strategy to answer a question like this—we’ll go over that later on. For now,
let’s just look at the correct and incorrect answer choices. In this example,
each of the two correct answer choices is supported by a different clue in the
sentence. Inconsequential to is supported by the fact that that the
unconventional political ideology has yet to gather enough support to…
replace existing ideologies. Deviant from is supported by the fact that the new
ideology has yet to be adopted by…existing ideologies. In this context,
however, both words give the same general meaning to the completed
sentence. Notice also the two synonyms, a threat to and foreboding to, lying
in wait for the unwary test-taker. These words may sound perfectly fine when
plugged into the sentence, but they do not correspond to the clues in the
sentence.
Of course, this doesn’t mean that synonym pairs are always the wrong answer
on Sentence Equivalence questions. In fact, the correct answers are often
synonyms. But, answering a Sentence Equivalence question by picking any
pair of synonyms is an unreliable strategy for conquering this portion of the
GRE. At best, focusing on synonyms can be a last-resort approach for
questions that you find difficult.
So, you ask, what is a good strategy?
Great question! We’re glad you asked.
THE BASIC APPROACH FOR SENTENCE
EQUIVALENCE QUESTIONS
The basic approach for Sentence Equivalence questions looks very similar to
the basic approach for Text Completion questions. Much like Text
Completion questions, Sentence Equivalence questions have clues and
transition words built in, and you should come up with your own word or
phrase for the blank before approaching the answer choices.
STEPS FOR SENTENCE EQUIVALENCE
QUESTIONS
1. Find the Clues and Transition words.
2. Come up with your own word or phrase for the blank. Write
that word or phrase down on your scratch paper.
3. Check each answer choice and use your scratch paper.
an answer that sort of matches your word
an answer that does not at all match your word
? any word you don’t know
CLUES AND TRANSITION WORDS
The first step in answering Sentence Equivalence questions is the same as that
for Text Completions. You must find the clues and transition words in the
sentence. Do not move on to Step 2 or look at the answer choices until you’ve
identified the clues and transition words in the sentence! Consequently, as
with Text Completion questions, much of your work for Sentence
Equivalence questions happens by examining the sentence itself before
considering the answer choices.
The clue is the words or phrases in the sentence that provide insight into the
word or phrase that goes in the blank. When reading a Sentence Equivalence
question and looking for the clue, ask yourself two questions:
•
Who or what is the blank describing?
•
What else in the sentence provides insight into that person or
thing?
Transition words are words such as and, but, so, however, because, despite,
since, although, instead, etc., that indicate how ideas in the sentence relate to
each other. Thus, transition words convey important information about the
intended meaning of a sentence. Some transition words, such as but and
however, indicate that the portion of the sentence immediately following the
transition word represents the opposite meaning to the other idea or action in
the sentence. Here are some examples of sentences employing these sort of
contrast transition words. The transition words are bolded.
I love coffee but I cannot tolerate the caffeine.
Although I love coffee, I cannot tolerate the caffeine.
Other transition words, such as and, because, and since, indicate that the
portion of the sentence immediately following the transition word represents
the same meaning as some other idea or action in the sentence. Here are some
examples of sentences employing these sort of same direction transition
words. The transition words are bolded.
I cannot tolerate caffeine, so I take my coffee decaffeinated.
Because I cannot tolerate caffeine, I take my coffee
decaffeinated.
Try out the basic approach to Sentence Equivalence questions on the question
we just saw:
Anthropologists contend that the ancient Mesopotamians switched from grain
production to barley after excessive irrigation and salt accumulation made the soil
____________ grains.
indifferent to
inhospitable to
unsuitable for
acrimonious to
benignant to
inured to
Here’s How to Crack It
Begin working on this question by first looking for clues and transition words
in the sentence. Ask yourself, “Who or what is the blank describing?” The
blank describes what the soil was to grains—the relationship between the
two. Now, ask yourself “What else in the sentence provides insight into that
person or thing?”, or, in this case, what else in the sentence provides insight
into the relationship of the soil to grains? The sentence states that ancient
Mesopotamians switched from grain production to barley and that excessive
irrigation and salt accumulation did something to the soil. These are the clues
for the sentence.
Now that you’ve identified the clue, look for any transition words. In this
sentence, the word after suggests that the switch from grain production to
barley is the consequence of irrigation and salt accumulation’s impact on the
soil. In other words, our two clues are in agreement and reflect the same
meaning.
With all this in mind, now move on to Step 2. Come up with your own word
or phrase for the blank that describes the effect on the soil’s relationship to
grains brought about by excessive irrigation and salt accumulation—an effect
that in turn would have caused ancient Mesopotamians to switch from grain
production to barley. If ancient Mesopotamians had to switch from grain
production to barley production, then excessive irrigation and salt
accumulation must have made the soil bad for grains in some way. So, use the
phrase “bad for” and move on to Step 3, checking the answer choices for any
choice that indicates something “bad for.”
Choice (A), indifferent to, does not mean something “bad for” so eliminate
(A). Choice (B), inhospitable to, is a good match for “bad for” because if the
soil was inhospitable to grain, it would explain why ancient Mesopotamians
switched from grain production to barley production. Put a checkmark next to
(B). Choice (C), unsuitable for, is also a good match for “bad for” as it would
also explain why ancient Mesopotamians switched from grain production to
barley production, so put another checkmark next to (C).
Don’t stop evaluating the answer choices just because you found two that
matched your word. Look at the remaining answer choices just in case
another answer choice also matches. If that is the case, then you will need to
reevaluate your interpretation of the sentence, or determine which words
produce sentences that are closest in meaning. Choice (D), acrimonious to,
may be a word you are unsure about, so put a question mark next to it. If you
happen to know that acrimonious means angry or bitter, then you can
eliminate this choice as not quite matching “bad for.” Choice (E), benignant
to, may also be a word you are unsure about, so put a question mark next to it
as well. Choice (F), inured to, is not a good match for “bad” as inured means
to grow accustomed to something, so eliminate (F).
You have two answer choices with checkmarks next to them, two choices
with question marks next to them, and two choices that are eliminated. Select
the two answer choices with checkmarks next to them, which is the correct
answer.
Nice work.
Sentence Equivalence Drill
Work the following questions, using the same approach outlined in this
chapter. Check your answers in Part V when you’re done.
1 of 5
To any observer, ancient or ___________, the night sky appears as a hemisphere resting on the horizon.
antiquated
perceptive
modern
astute
contemporary
archaic
2 of 5
Researchers interested in the nature versus nurture debate use identical twins who were separated at
birth to explore which personality characteristics are ____________ and which arise through
experience.
intractable
nascent
erudite
innate
predilection
inborn
3 of 5
The eccentric Canadian Prime Minister, Mackenzie King, often used séances to contact his dead pet dog
for advice; despite this ____________ behavior, the public had so much confidence in his ability as a
leader that he was in power for 22 years.
capricious
lackluster
poised
unconventional
repulsive
decorous
4 of 5
The circulation of the blood makes human adaptability to the ____________ conditions of life, such as
fluctuating atmospheric pressure, level of physical activity, and diet, possible.
inveterate
dynamic
timorous
cowed
turgid
oscillating
5 of 5
Arriving in New Orleans days after Hurricane Zelda had passed and without an adequate number of
vehicles of its own, the armed forces began to ____________ any working form of transportation they
could find, including a bus that had been chartered at great expense by a group of tourists.
repatriate
commandeer
extradite
interdict
expurgate
appropriate
LET’S TALK ABOUT VOCABULARY
The basic approach for Sentence Equivalence questions is going to be useful
for each Sentence Equivalence question on the GRE. You’re going to need to
know how to proceed once you encounter a question. Knowing and believing
in the basic approach is extremely valuable.
But, the basic approach can only get you so far. The truth is, for some
Sentence Equivalence questions, if you do not know the meanings of the
words in the answer choices, you’ll likely end up guessing. There is only one,
sure-fire defense against the possibility of guessing. That defense is having a
robust vocabulary.
At the end of this section, we discuss in more detail vocabulary on the GRE.
We have included the Key Terms List, which is a list of the words most
commonly seen on the GRE. You should learn these words to stand the best
chance of knowing many of the words you’ll see on the GRE.
One of the best ways to help learn vocabulary, and to shed some light on
unfamiliar words, is by understanding the roots of words.
Word Roots
Word roots are linguistic units that have distinct meanings. They’re
building blocks for words in modern English. Mastery of word roots can
accelerate your vocabulary improvement. A knowledge of word roots
can also sometimes help you infer enough about a mystery word to
decide whether to keep or discard it as an answer choice. Here’s a
smattering of common word roots:
•
ben or bene—good: benefit, benefactor, benediction.
•
mal or male—bad: malign, malfeasance, malediction.
•
anthropo—having to do with humankind: anthropology,
philanthropy, anthropocentric.
•
cise or cide—strike, cut, or kill: incisive, circumcise,
homicide.
•
gen or gene—origin, kind or type: genesis, generate, genus,
homogenous.
•
morph or morpho—form or shape: morphology, amorphous,
metamorphosis.
•
vol or voli—will or intention: volunteer, voluntary, volition.
Word roots are often combined. From the roots listed above you can now
decipher several GRE-level words: benevolence (good intention),
malevolence (bad intention), anthropogenic (caused by human activity),
anthropomorphic (taking human form), morphogenesis (how something
takes form), genocide (killing an entire group of people).
Prefixes and suffixes are especially common word roots. Just a handful
of the prefixes you’re sure to encounter: ante (before), anti (against),
circum (around), hyper (over, above), trans (across). And here are some
common suffixes: able (for adjectives indicating capability), ism (for
nouns denoting a doctrine or belief), less (for adjectives indicating
absence of something), ly (used to form adverbs from adjectives).
One good way to learn word roots is by noting the etymology (origin) of
words that you look up in the dictionary. Look for word roots in your
Key Terms List (in Chapter 8) and any other new words you learn.
But, learning the entirety of the Key Terms List or memorizing a couple of
word roots, is in no way comprehensive. The GRE can test any word it wants,
so unless you have a full working knowledge of the dictionary, its likely
you’ll come across some words on test day that you are unfamiliar with.
That’s okay.
In the following section we’re going to outline for you some strategies for you
to fall back on in case you are unsure how to proceed with a particular
question, and you don’t know what the words mean.
It’s worth repeating here that the top strategy for all Sentence Equivalence
questions is first to determine whether you know the words. Test-takers too
often make the mistake of believing that the strategies suggested below are a
cure-all (or, to use the GRE vocabulary, a nepenthe) for their Sentence
Equivalence problems. We want to be very clear about this: there is no
substitute for a killer vocabulary.
These strategies may not result in eliminating all the incorrect answer choices.
But, if you can eliminate some, your chances of guessing correctly are
certainly improved.
A PIECE OF ADVICE
When you come across a Sentence Equivalence question on test day, follow
the basic approach. But, when you begin to evaluate the words in the answer
choices the best thing you can do is be honest with yourself. If you don’t
know any of the words, then start thinking about some of the Process of
Elimination strategies below. When confronted with a word they do not know,
many test-takers will make the mistake of stubbornly staring at the word,
convinced that if they continue to stare the word’s meaning will appear. This
behavior wastes valuable time that could be spent dealing with other
questions and words that they do know.
So, on test day, if you don’t know a word, just admit it and move on to
process of elimination strategies. Or, if you don’t know the meanings of most
or all of the words in the answer choices, make a guess and move on to the
next question.
PROCESS OF ELIMINATION STRATEGIES
Ideally, when you encounter a Sentence Equivalence question, you are able to
discern the clues in the sentence clearly and come up with a spot-on word for
the blank. Ideally, too, you will know the meaning of every answer choice.
Needless to say, this ideal scenario isn’t the only situation you will come up
against when working through the Sentence Equivalence questions in the
verbal sections of the GRE. The precise nuance of the clues may elude you,
making it hard to come up with a word for the blank. Or you may find
yourself fuzzy, or even downright clueless, about the definition of some of the
answer choices. Fret not. This happens to everyone!
Luckily, with two correct answer choices and four wrong ones, there are
many opportunities for effective use of Process of Elimination. Let’s look at a
few of the POE strategies and considerations available to you.
Positive and Negative Words
One way to slice quickly through the lineup of answer choices is to decide
whether the word in the blank should have a positive or negative connotation
and then separate the answer choices into positive ones and negative ones.
You don’t need to know the exact dictionary definition of every answer
choice if you can somewhat confidently identify it as positive or negative.
However, note that with the exception of words such as “sizzle” words do
NOT have meanings that relate to their sounds. So, don’t fall for the trap of
saying something like “Oh, that word sounds ugly so it must be a negative
word.” After all, pulchritude isn’t a particularly nice sounding word but it
means beauty. So, you can’t separate words that you’ve never encountered
before into positive or negative. But, you may remember that a word you’ve
studied has a negative meaning even though you can’t remember the precise
meaning of that word.
Let’s practice using this approach on the following question:
Despite the implications of their noble status, many aristocrats were virtually
penniless and lived in a state of ____________ .
indigence
opulence
eminence
penury
depravity
complacency
Here’s How to Crack It
The transition word that begins this sentence, despite, tells us that the state in
which many aristocrats…lived is the opposite of their noble status. Because
noble status is a positive idea, the word in the blank should be negative. This
is reinforced by the additional clue that many aristocrats were virtually
penniless. Evaluate the answer choices one at a time, eliminating positive
words and holding onto negative words.
Choice (A), indigence, is an uncommon word. Instead of spending time trying
to decipher whether it’s positive or negative, just mark it with a question mark
and move on. Choice (B) is another uncommon word, opulence, so give that
one a question mark as well. Choice (C), eminence, is a positive word—think
of someone described as an eminent doctor or as an eminent author.
Therefore, eliminate (C) because the word in the blank has to be negative.
Choice (D), penury, is another uncommon word, so mark it with a question
mark. Choice (E), depravity, means moral corruption. This is certainly a
negative word, but would you describe a penniless person as depraved? Not
likely, so eliminate (E) as well. The final word, (F), is complacency, which
means a feeling of self-satisfaction, so eliminate (F).
After all that, you have three answer choices remaining—(A) indigence, (B)
opulence, and (D) penury. This is a much better situation than guessing from
among all six. And if you happen to know that the word opulence is a positive
word suggesting luxury, you’ve got the answer—it has to be (A) and (D).
Let’s move on to another strategy.
Synonym / No Synonym
One strategy is to look over the answer choices for synonym pairs and choose
one of these pairs for the answer. However, the warning given earlier in the
chapter still holds: It is sometimes the case that the correct answer choices
will not be strict synonyms while synonym pairs can be found among the
incorrect answer choices! Therefore, this strategy must be used with caution
and considered a last resort. It’s best reserved for times when you are pretty
familiar with the words in the answer choices but having difficulty with the
clue.
Consider this example:
Because mercury has a variety of innocuous uses, including in thermometers and
dental fillings, few people realize that it is one of the most ____________
substances on the planet.
acidic
irritating
mundane
deleterious
disagreeable
pernicious
Here’s How to Crack It
The clue here may be confusing, making it hard to come up with a word for
the blank. So work with the answer choices to pair those that are synonyms
and eliminate those with no synonyms. Evaluate the answer choices one at a
time.
Start by eliminating (A), which has no synonyms among the other answer
choices. Choice (B) is irritating. Scanning the other answer choices for a
synonym, you’ll find (E), disagreeable. If one of these is correct, the other is
likely to be as well, so make them a pair. Choice (C) is mundane, which can
mean either worldly or unexciting. This has no synonym among the other
answer choices, so eliminate (C). Choice (D) is deleterious, a word similar in
meaning to (F), pernicious, the only word remaining. Make these another pair.
This process eliminates two choices and leaves you with two pairs of
synonyms. Guessing at this point will give you a 50/50 chance of getting the
correct answer. If you’ve searched for the clue and come up empty-handed,
those are not bad odds.
Here’s how to choose between the answer choices. The blank should describe
what kind of substance mercury is. The sentence gives the insight that
mercury has a variety of innocuous or harmless uses. The transition word
because suggests agreement between this clue and the blank. However, the
sentence contains another transition in the phrase few people, which indicates
that the word in the blank should actually be the opposite of innocuous. This
insight makes the correct answer (D) and (F).
ADVANCED SENTENCE EQUIVALENCE
QUESTIONS AND HOW TO CONQUER THEM
With Text Completion questions, we saw that GRE ups the difficulty by
creating questions with multiple blanks. Some of these questions might even
have two or more sentences! Neither of these complications occurs in
Sentence Equivalence questions—they are always a single sentence
containing a single blank. For Sentence Equivalence questions, the writers
have some other tools to make questions difficult.
Difficult Transitions. When we introduced the topic of transitions, we
focused on words such as and, but, so, however, because, despite, since,
although, instead, etc. But not all transitions are marked by the obvious words
that typically serve this function. Be on the lookout for less-than-obvious
transitions. A transition can be any language indicating that two parts, ideas,
or actions in the sentence are the same or opposite in sense. Let’s consider
these examples:
Being a confirmed coffee snob, Boris
_________________ the foul gas-station brew.
reluctantly
Being a confirmed coffee snob, Boris surprised me by
________________ the foul gas-station brew.
The clue in both sentences is that Boris is a coffee snob. In the first sentence,
the adverb reluctantly implies that whatever he did with the gas-station brew
was the opposite of his inclination. In the second sentence, the fact that
Boris’s actions were surprising again implies an action that is the opposite of
the clue. In both cases, Boris has acted against his nature as a coffee snob.
Therefore, the word in the blank should suggest that Boris was willing to
drink the foul gas-station brew.
For another example, consider the use of few people in the mercury example
used in the previous section, on this page. There are many ways for a sentence
to present things as the same or opposite, as agreeing or contrasting, as similar
or different. Read carefully and critically!
Secondary Definitions. Sometimes the folks at ETS will make a question
harder the old-fashioned way: with harder vocabulary.
There’s no getting around it—your best defense against a lineup of scary
answer choices is a formidable vocabulary. But it’s not just about learning
those polysyllabic, arcane, and unusual words. Many common words have
less-common meanings or nuances that may be exploited on the test. The verb
apprehend, for example, usually means to catch or arrest a wrongdoer. But it
may also simply mean to perceive or to understand. While the verb realize
commonly means to become fully aware of something, it can also mean to
make something a reality. The adjective fast may describe something speedy
or something fixed securely in place. And, as a verb, flag can mean to mark
with a flag or to become droopy or tired. Moral of the story: When you learn a
new word, take the time to learn the secondary and tertiary definitions as well.
Tips for Advanced Sentence Equivalence. Our tips for conquering the most
difficult Sentence Equivalence questions fit within the three steps of the basic
approach:
1. Find the Clues and Transition words.
•
Begin by asking “Who or what is the blank describing?”
and “What else in the sentence gives insight into that person
or thing?
•
For Sentence Equivalence questions it may be difficult to
identify the clue using the questions above. If that is the
case, then start by determining the part of speech needed in
the blank. This helps you to more concretely and efficiently
answer the question, “Who or what is the blank
describing?”
•
Transitions are not always clearly marked with words such
as and, but, so, however, because, despite, since, although,
instead, etc. Be alert to other ways that a sentence can make
two parts the same or opposite, agreeing or contrasting.
2. Come up with your own word or phrase for the blank.
•
The more thoroughly you’ve done Step 1, the easier it will
be to come up with a word for Step 2, and the better that
word will predict the correct answer choices.
•
Do not be preoccupied with coming up with the perfect,
most GRE-worthy word. Feel free to recycle from the clues
in the sentence. Use a phrase instead of a single word. You
do want a word or phrase that accurately reflects the clues.
But your goal is not to have a scratch pad full of elegant
words; it’s to answer the questions quickly and correctly.
3. Check each answer choice and use your scratch paper.
•
Stick with the clues and the word you come up with. In
reviewing the answer choices, if you have to choose
between words you know that don’t match and words you
don’t know, pick from the words you don’t know! For
example, if you have eliminated three answer choices and
put question marks next to the other three, pick two from
the ones that you’ve marked with question marks.
•
What makes a Sentence Equivalence question harder is
often just the difficulty of the words in the answer choices.
Your best defense is to build a strong vocabulary. Learn
your word lists, and learn the range of meanings for each
word.
•
The correct answer will not always be a pair of synonyms,
and synonym pairs in the answer choices are not necessarily
the correct answer. See the Cautionary Tale on Synonyms at
the beginning of this chapter.
Let’s put these advanced skills together in working through some more
difficult questions.
Despite their outward negativity, many a cynic harbors an inner faith in the
_____________ of humankind.
benevolence
precocity
parsimony
ignobility
antipathy
probity
Here’s How to Crack It
Find the clue for this Sentence Equivalence question by asking, “Who or what
is the blank describing?” If the answer to that question is unclear, then
determine the part of speech to more easily answer the question. In this case,
the blank is a noun describing some aspect of humankind that cynics have
faith in. Now ask, “What else in the sentence gives insight into that person or
thing?” This clue comes from the introductory phrase, [d]espite their outward
negativity. Despite is a transition word suggesting that their outward
negativity is the opposite of their inner faith in some aspect of humankind.
Therefore, the blank must refer to some positive aspect of humankind. Pick an
appropriate word such as the “good” of humankind for the blank, or focus on
positive words in the answer choices. Evaluate the answer choices
individually.
Choice (A), benevolence, is a positive word so keep (A). Choice (B),
precocity, is an uncommon word, so put a question mark next to this one. The
same can be done for (C), parsimony. Choice (D) has the root word noble in
it, which is certainly positive, but the prefix ig makes it a bad thing—think of
the word ignorant. Eliminate this choice. Choice (E) has the prefix anti-,
meaning against. This generally implies something negative, so eliminate (E).
Choice (F), probity, is another tough word, so put a question mark next to it.
At this point, select (A), as it is the only choice with a checkmark next to it.
Choices (B), (C), and (F) all have question marks, so if there is no way to
further parse out what those words mean, pick one of them to go with (A) and
move on. At the worst, you have a 1-in-3 choice of guessing correctly. Taking
the POE a little further, you should also be able to eliminate (B). The word
precocity is related to precocious. It also begins with the prefix pre-, meaning
before—an idea that’s neither positive nor negative. Choice (C), parsimony,
means frugality, and (F), probity, means honesty and integrity. Thus, the
correct answer is (A) and (F).
Let’s try one more:
Formerly seen only on sailors and bikers, tattoos in the United States have become
so ____________ in urban culture as to lose any rebel cachet.
prepossessing
fascinating
pedestrian
peripheral
marginal
pervasive
Here’s How to Crack It
Find the clue by asking first, “Who or what is the blank describing?” If the
answer to that question is unclear, then determine the part of speech to more
easily answer the question. In this case, the blank is an adjective describing
what tattoos have become…in urban culture. Now ask, “What else in the
sentence gives insight into that person or thing?” Clues here are that they
were [f]ormerly seen only on sailors and bikers and that, as a consequence of
what they’ve become, they have lost any rebel cachet. The word formerly is a
transition word suggesting that tattoos—or specifically their cultural
significance—have changed in some way. Therefore, the blank should suggest
the opposite of being seen only on sailors and bikers. A good word might
simply be “common,” so use that for evaluating the answer choices. Evaluate
the answer choices individually, looking for reasons to eliminate each.
Choice (A), prepossessing, might be unfamiliar. Trying to determine the
meaning from its parts, you’d come up with something like “owning before.”
It’s hard to see how this matches “common,” so eliminate (A). Choice (B) is
fascinating. While modern culture may be fascinated with tattoos, it doesn’t
match the word “common,” so eliminate (B). Choice (C) is pedestrian. As an
adjective, pedestrian can mean either walking on foot or ordinary. In the
sense of ordinary, this is a good match for “common,” so put a checkmark
next to (C). Choice (D), peripheral, means at the edge of something—not a
match for “common.” Eliminate (D). Choice (E), marginal, means the same
thing as peripheral, so eliminate it as well. The final choice is (F), pervasive,
which describes something that is found everywhere. This could be another
way of saying “common,” so (F) earns a checkmark. The answer is (C) and
(F).
Notice some pitfalls that we’ve avoided in this question. Two of the answer
choices, peripheral and marginal, are synonyms but don’t match “common.”
They’d be tempting if you missed the time transition implying that tattoos
have changed from being something unusual. The words prepossessing,
meaning impressive or pleasing, and fascinating are another decoy synonym
pair. The correct answer choices, pedestrian and pervasive, aren’t strict
synonyms. Furthermore, recognizing pedestrian as a correct choice depends
on knowing its secondary definition. These are all traps that might have
tripped you up before, so you’ve learned a lot!
Sentence Equivalence Practice Set
Work the following questions, using all the techniques you’ve learned for
Sentence Equivalence. Check your answers in Part V when you’re done.
1 of 5
Possessed of an insatiable sweet tooth, Jim enjoyed all kinds of candy, but he had a special
____________ for gumdrops, his absolute favorite.
affinity
odium
nature
disregard
predilection
2 of 5
Although the Wright brothers’ first attempted flight in 1901 was a ____________ and subsequent efforts
similarly ended in failure, they persisted and ultimately made the first successful airplane flight in 1903.
fiasco
debacle
hindrance
feat
triumph
precedent
3 of 5
The fuel efficiency of most vehicles traveling at speeds greater than 50 miles per hour ____________ as
the vehicle’s speed increases, due to the increased aerodynamic drag placed on the vehicle.
equalizes
adapts
stabilizes
diminishes
increases
wanes
4 of 5
Despite the vast amount of time Francis dedicated to learning six different languages, he was
____________ communicator; his mastery of vocabulary and grammar failed to redress his inability to
construct cogent prose.
a florid
an inept
a prolific
an astute
a morose
a maladroit
5 of 5
The twins’ heredity and upbringing were identical in nearly every respect, yet one child remained
unfailingly sanguine even in times of stress while her sister was prone to angry outbursts that indicated
an exceptionally choleric ____________ .
genotype
environment
physiognomy
incarnation
temperament
humor
Summary
The approach for Sentence Equivalence questions is the same as for
Text Completions. Ignore the answer choices, ask who or what the
blank is describing, look for clues and transition words, fill in your own
word for the blank, and check the answer choices against your word
using POE. You must pick two answer choices.
Identifying the part of speech that should go in the blank will help
answer who or what the blank is describing.
Pay close attention to transitions. Transitions indicate two parts of the
sentence are the same or opposite in meaning. They are often marked
by obvious words like and, but, so, however, because, despite, since,
although, instead, etc. Other transitions are not as obvious but still
important.
If the clue is hard to decipher, you can simplify POE by determining if
the word to go in the blank should be positive or negative. Then narrow
down the answer choices by eliminating those that don’t match.
The two correct answer choices may not be strict synonyms.
Sentence Equivalence questions can be made harder simply by having
more difficult words in the answer choices. Keep working on
vocabulary every day! Learn prefixes, suffixes, and other word roots.
Chapter 6
Reading Comprehension
Reading Comprehension questions on the GRE can be quite deceptive. On the
one hand, the answer to each question is somewhere in the passage. On the
other hand, ETS is really good at crafting answers that seem right but are, in
fact, wrong. This chapter will teach you the best way to approach the reading
passages on the test and how to attack the questions. Furthermore, you’ll learn
how to use Process of Elimination to get rid of wrong answers and maximize
your score.
WHAT YOU WILL SEE
On the GRE, you’ll have about eight reading passages, varying in length from
a mere 12 lines to more than 50 lines. After each passage, you’ll be asked to
answer a number of questions. Your task is to choose the best answer to each
question based on what is stated or implied in the passage. Translation: The
correct answer to every question is somewhere in the passage. In fact, think of
Reading Comprehension questions as an open-book test. Your goal is simply
to locate the answer within the passage.
Reading Comprehension
is like an open-book test:
The correct answer to
every question is somewhere in the passage.
Reading Comprehension and the Computer
Reading Comprehension questions are presented on a split screen. The
passage is on the left side and stays there while you work on the questions;
you may have to use the scroll bar to read the whole passage. The questions
appear one at a time on the right side. It’s very important to practice reading
comprehension on the computer with The Princeton Review’s online practice
tests or ETS’s free POWERPREP® II software (see Chapter 1), because you’ll
have to get used to not being able to circle or underline words, bracket text,
write notes in the margin, and so on. But you can start practicing good habits
right now. As you work through this chapter, and any time you practice
reading comprehension on paper, don’t allow yourself to write on the passage.
Anything you write must be written on scratch paper. In your preparation for
the GRE, never give yourself a crutch you won’t actually have when you take
the real test.
Let’s get started.
Online Practice Tests
Where are those online
practice tests, you ask?
They’re in your Student
Tools found at
PrincetonReview.com.
You must have registered
your book by now, so logging in will be a breeze!
READING AND THE GRE
Although it might seem that Reading Comprehension questions shouldn’t be
very hard, ETS makes these types of questions difficult by exploiting some
common assumptions.
The reading skills you’ll need to use for Reading Comprehension questions
on the GRE are quite different from the ones you use in your everyday life.
The biggest challenge will probably be the limited time you have to answer
the questions.
For one thing, ETS (intentionally) chooses reading passages that are
complicated and are concerned with unfamiliar and, in some cases,
intimidating topics, hoping that you’ll have a tough time absorbing the
entirety of the passage in the short amount of time they give you. In many
cases, that is exactly what happens: Test takers spend too much time trying to
understand what they’ve read and not enough time working on the questions.
ETS also hopes that you will overanalyze the text. This level of critical
thinking is wholly appropriate for most types of academic reading, but on the
GRE it only leads to trouble. The way to crack the reading portion of the GRE
is to read less into the passages, not more.
Although it may sound counterintuitive, in some ways the passage itself is the
least important part of Reading Comprehension questions. This is for a simple
reason—you don’t get any points for reading the passage, and the only way to
do well on the GRE is to amass as many points as possible.
Okay, now you’re ready to take a look at our approach to Reading
Comprehension questions.
The Directions
These are the directions you may see on the GRE:
Directions:
Each passage in this group is followed by questions based on its content. After reading a
passage, choose the best answer to each question. Answer all questions following a
passage on the basis of what is stated or implied in that passage.
Here are our directions:
Directions:
This is not really a test of reading, nor is it a test of comprehension. It’s a treasure hunt!
You can find all of the answers in the passage.
READING COMPREHENSION: THE BASIC
APPROACH
1. Attack the Passage. This step will vary slightly based on the
length of the passage you’re dealing with, but in each case, the goal
is to read less, not more.
2. Size Up the Questions. Reading Comprehension questions on the
GRE can ask you to do a variety of things. Make sure you know
what the question’s asking you to do.
3. Find and Paraphrase the Answer. This is the key. Always return
to the passage to find your answer; never answer questions from
memory!
4. Use Process of Elimination. You can use a number of helpful POE
guidelines on Reading Comprehension questions. We’ll go over
these in detail in a moment.
Let’s look at each step in some more detail.
ATTACK THE PASSAGE
Imagine you drop out of an airplane and land on a random college campus.
You walk into a random building, pop into the first lecture hall you see, and
stand in the back for ten minutes. When you come out, someone asks you a
bunch of questions about what you’ve just heard. That is what reading
comprehension is like on the GRE. You don’t pick the topic; you don’t start
from the beginning; there is no title, no outline, and no table of contents. You
are not in control.
Remember!
You don’t have to read
every single word of
the passage in order to
answer the questions.
The creators of the GRE are going to give you short and long passages filled
with tons of information that you will never be tested on. They will try to
suck you into these dense, badly written science or humanities passages in
order to get you to waste time and to confuse you with useless information.
Your job is to read as little of the passage as you need to get started on the
questions and then to let the questions tell you which facts to care about. To
get started on the questions, you need to know only the main idea of the
passage, the structure, and the tone.
Fortunately, you know most of this already. The truth is that all GRE passages
are really about one of two things: a problem or a change. You may think a
passage is about art history or geology or different kinds of rocks on Jupiter,
but really, it’s either about a problem or a change.
Furthermore, once you know whether it is about a problem or a change, you
even know what the passage is likely to cover.
Problem passages cover these questions:
1. What is the problem?
2. What caused the problem?
3. What are the effects of the problem?
4. Are there any solutions?
Change passages cover these questions:
1. What was the old way?
2. What is the new way?
3. What caused the change?
4. What are the effects of the change?
Knowing how passages are organized will change the way you read. This
information puts you back in control by allowing you to categorize the
information you’re given and to anticipate what is coming next. Remember:
On the first reading, you just need the basics. Don’t get sucked into details
you don’t need to know.
Once you know whether a passage is about a problem or a change, you just
need enough information to answer the four standard problem or change
questions. Feel free to skim the rest. If you are asked a question about
something you skimmed over, you can always go back to find it.
There is one golden rule of reading comprehension: Always go back to the
passage to find proof. If you cannot put your finger on a line that proves your
answer choice, you should not pick it.
When you see reading comprehension passages, practice categorizing them as
problem or change, and then practice anticipating what each paragraph is
going to be about. Once you get good at this, you will find that you are in
control, not them.
Try reading the following passage:
Prior to 1735, there was no legal precedent for freedom of the press. The
constitutional concept of freedom of the press traces its origins to 1735 and the
libel trial of John Peter Zenger. Zenger, born in Germany, emigrated to
America in 1710 and established The New York Weekly Journal in 1733. The
Journal starkly opposed the policies of New York governor William Cosby and
while Zenger did not write the majority of the critical pieces, he was arrested
on libel charges in 1734. In the ensuing trial, widely followed by the populace,
Zenger was defended by Andrew Hamilton, a Pennsylvania lawyer who was
brought in after Cosby disbarred all the New York lawyers who offered to
defend Zenger. Hamilton’s brilliant defense of Zenger was predicated on the
argument that since Zenger’s criticisms involved verifiable facts, they could
not possibly be considered libel. The judge agreed and acquitted the publisher,
establishing the basic concept of freedom of the press that was to be enshrined
in the United States Constitution some 57 years later.
Problem or change?
What was the old way?
What is the new way?
What caused the change?
What are the effects of the change?
Yes, the preceding passage is about freedom of the press, but it’s really about
a change. According to the old way, there was no freedom of the press, and
reporters could be arrested. After the adoption of the new way, reporters
writing verifiable facts could not be charged with libel. The cause of the
change was the trial of John Peter Zenger, and the effect of the trial was the
precedent of freedom that eventually became enshrined in the U.S.
Constitution some 57 years later.
If you said that a lack of freedom of the press was a problem, don’t worry. It
was. The important thing is that you were the one in charge when you were
reading, and you were the one asking the questions. Instead of passively
letting information wash over you, hoping the important parts of the passage
would stick, you became an active reader.
Now try again on a longer passage. Remember not to get bogged down by the
details in the passage. Read for evidence of what the author thinks. Important
statements in the passage contain the author’s opinions, recommendations,
and conclusions.
Stay focused on finding
the main idea as you read.
What was it about Oscar Wilde’s only novel, The Picture of Dorian Gray,
that caused it to create such an uproar when it was published in 1891? While
critics attacked the quality of Wilde’s work, lambasting its plot as “incurably
silly” and chiding the writer for using prose that was “clumsy” and “boring,”
these overt denunciations of the formal elements of Wilde’s work merely
masked the true concerns of many nineteenth-century critics. What these
critics were actually railing against was the thematic content of Wilde’s work,
specifically his illustration of a lifestyle devoted to useless beauty. For many a
nineteenth-century moralist, The Picture of Dorian Gray was nothing more
than a primer for spiritual depravity. Wilde’s ultimate sin was not his clunky
plot or his sometimes cloying prose; it wasn’t even his disregard for the timehonored tradition of English propriety. It was instead his leniency toward his
protagonist. Wilde propagated the disdain of critics not simply because Dorian
Gray was an unabashed hedonist, but because Wilde failed to punish his
subject appropriately for his hedonism. To the critics, allowing an evil
character to escape his just deserts was an unforgivable sin, and it was this
transgression that resulted in such opprobrium for Wilde’s work. In their mind,
Wilde’s work was corrupting the genteel reading public by failing to show the
proper consequences of immoral behavior.
Problem or change?
What is the problem?
What caused it?
What are the effects?
Are there any solutions?
Here we have a longer passage about the critical response to Oscar Wilde’s
The Picture of Dorian Gray. You know that it is a problem in the very first
sentence when you are told that the novel created “an uproar” and in the
second sentence when you are told that critics “attacked” it. The cause of the
problem doesn’t come until the last third of the passage. The protagonist was
a hedonist, but Wilde did not punish his character for his sins. The effect of
this problem was the outrage from critics. No solution is offered. Everything
else is just details. Transitions such as Wilde’s ultimate sin and It was instead
are good indicators that something important is being said.
Purpose
You will often see questions that ask about an author’s purpose—that is, why
the author bothered to write the passage, paragraph, or sentence at all.
Purpose can be summed up with the acronym PRICE. The purpose of a
paragraph, passage, or even an individual sentence is to Predict, Recommend,
Inform, Correct, or Evaluate.
Most passages or paragraphs simply inform. Whenever an author begins to
offer an opinion, however, he or she may be evaluating an argument,
correcting a misperception, predicting an outcome, or even recommending a
behavior.
With longer passages, it is helpful to go paragraph by paragraph and note the
subject (the old way, the new way, the nature of the problem, and so on) and
the purpose of each paragraph. Jot this information down on your scratch
paper. Doing so will force you to actively assess each paragraph and will give
you a map that you can use to find the answers for specific questions.
Here is a longer passage to try.
Make sure that you scroll
down as far as you can, to
guarantee that you see
the entire passage.
Scientists researching the aging process are increasingly investigating the
role of telomeres, portions of DNA on the ends of chromosomes found in every
cell. The exact relationship between telomeres and aging is unknown. Unlike
the rest of the chromosome, telomeres do not contain genes, the strands of
DNA that code for particular enzymes and proteins. Telomeres primarily serve
a protective role in cells, playing two key roles in maintaining healthy cells.
First, telomeres prevent important genetic material from being lost during cell
replication, functioning as a “cap” of sorts on the end of each chromosome.
Second, telomeres serve as a biological marker that the chromosome is
“complete”; without a telomere on the end of a chromosome, the body
considers the chromosome defective and takes steps against it.
While the protective role of telomeres is fairly well understood, scientists
are interested in another facet of telomeres. Telomeres contain between one to
two thousand copies of a particular DNA sequence. Each time a cell divides, a
minuscule bit of this DNA sequence is lopped off. When telomeres become too
short, the cell becomes impaired, unable to divide, and prone to malfunction.
Cells with critically short telomeres eventually die, leading many researchers
to compare telomeres to biological clocks or fuses, counting down to the death
of a cell.
Although the role of telomeres in cellular aging and malfunction is well
documented, new research is focused on searching for a link between cellular
aging and aging and disease in humans. One study has found that subjects with
shorter telomeres are more likely to develop cancers of the lungs and kidneys
than those with longer telomeres. Furthermore, the study noted that the
participants with the shortest telomeres were at a higher risk of developing
heart disease and also appeared more prone to infectious diseases. Another
study posited a link between telomere length and life span. In that study,
patients with shorter telomeres died about 4 or 5 years earlier than those with
telomeres of greater length.
Of course, many researchers are hesitant to conclude that shorter
telomeres are a causative factor from this data, particularly because telomeres
are susceptible to corruption from a number of factors besides cell division.
For example, scientists have noted that telomeres are especially vulnerable to
the byproducts of the body’s oxidation process, by which oxygen is converted
to energy. The byproducts of this process, called free radicals, can not only
harm cells and DNA, but also artificially shorten telomeres.
Further research is necessary to better establish what link, if any, exists
between telomeres and aging. One promising avenue to consider is whether
lengthening damaged telomeres has the opposite effect on subjects, making
them healthier and conferring greater longevity. And while some scientists
optimistically believe that a full understanding of telomeres will eventually
bestow dominion over the very aging process itself, such a scenario is both
unlikely and not technologically feasible at this juncture.
Problem or change?
What was the problem?
What caused it?
What were the effects?
Is there any solution?
The preceding passage is a long science passage with lots of technical
information. In essence, however, it is about a problem. Scientists think that
there is a link between telomeres and aging, but they don’t know. The cause
of the problem is that there is a link between the length of a telomere and the
health of cells. The effect of this problem is lots of studies showing links
between telomeres and different health problems. The solution, of course, is
more research. The exact relationship is still unknown.
When you map the passage, paragraph by paragraph, you should come up
with something like this:
Paragraph 1: What’s a telomere? (Inform)
Paragraph 2: Shorter telomere = dead cell (Inform)
Paragraph 3: Effects of shorter telomeres (Inform)
Paragraph 4: Caution against conclusion (Inform)
Paragraph 5: Possible effects of finding link (Predict). Beating aging unlikely
(Evaluate)
That is as much information as you need to answer Main Idea and Purpose
questions, and as much as you need to get started on specific questions. If a
question asks about the connection between telomeres and cell health, you
know where to go. Until then, feel free to skim over the details.
Need More Verbal
Help?
Check out The Princeton
Review’s Verbal Workout
for the GRE for more Text
Completion, Sentence
Equivalence, and Reading
Comprehension practice.
SIZE UP THE QUESTIONS
Reading Comprehension questions vary in both format and what they require
you to do. Let’s take a look at the different types of questions you’ll see on
test day, and then go through strategies for tackling each type.
Question Formats
The Reading Comprehension questions on the GRE will appear in several
different formats.
1. Multiple Choice. These are the standard, five-answer multiplechoice questions that ask you to choose a single answer.
2. Select All That Apply. These questions ask you to select more
than one answer, similar to the way you answered Sentence
Equivalence questions.
3. Select in Passage. These questions either refer you to a highlighted
portion of the text or ask you to click on the portion of the text that
contains a certain phrase or performs a certain function.
Question Tasks
While it might seem like there are tons of different reading comprehension
tasks, there are really only two major types on the GRE.
1. “Fetch” Questions. Some questions simply require you to go to
the passage and “fetch” some information. The information you are
asked to fetch might be a fact from the reading, the meaning of a
word, the author’s tone, or the main idea of the passage.
2. Reasoning Questions. Other questions require a little more work
than just returning to the passage and figuring out what the author
says. Reasoning questions can ask you why an author used a
particular word or sentence, what inferences you can draw from the
passage, or who the author’s intended audience may be. Reasoning
questions may also ask critical reasoning-style “argument”
questions about conclusions, premises, and assumptions.
Each of these question tasks may show up in any of the question formats
above. Let’s look at some of these questions in more detail.
The answer to a
Reading Comprehension
question has to be
supported by the passage.
Fetch Questions
Fetch, or retrieval, questions ask, in one form or another, “What does the
passage say?” They are the most straightforward of reading questions, and
simply require you to return to the passage and retrieve information. To
answer a retrieval question, use the following steps:
1. Read the Question. What kind of question are you dealing with?
2. Make the Question Back into a Question. Often the questions
aren’t questions at all; they’re really incomplete sentences. To find
an answer, you must first have a question. By putting the question
into your own words, you interact qualitatively and actively with
the question text. There is no possibility of your eyes glazing over
or your brain going on autopilot (a real likelihood with a four-hour
exam). To make the question into a question, simply start with a
question word. Nine out of ten times What or Why will work, since
most questions ask either what was said in the passage or why it
was said.
3. Find Proof. This is the golden rule of reading comprehension. You
will always be able to prove the correct answer with something in
the passage. If you cannot put your finger on a specific word,
phrase, or sentence that proves your answer choice, you can’t pick
it. To help find answers in the passage, use one or both of the
following techniques:
a.
Five Up/Five Down. You can’t trust ETS to put the correct
answer exactly where they say it will be. If they highlight a
portion of the passage, start reading five lines above and
read until five lines below the highlighted passage. This
way, you are always looking at things in context.
b.
Lead Word. A lead word is any word in the question that
will be easy to skim for in the passage. Names, numbers,
dates, large technical terms all make good lead words. Of
course, once you find your lead word, read five lines up and
five lines down (for a vocab-in-context question, you need
to read only three lines up and three lines down).
4. Link the Info in the Passage to the Question Task. Once you find
the relevant information in the passage take a moment to make sure
that it addresses the question task. Is this all the author said? Are
there other details that you need to consider?
5. Use Process of Elimination.
a.
Avoid Extreme Statements. No matter what the passage
says, ETS can phrase a correct answer any way they like.
They want correct answers that are difficult to argue with.
That means wishy-washy language (often, many, usually).
Extreme language (is, all, every, always) is too easy to
prove wrong, so it almost always is incorrect.
b.
Recycled Language. ETS knows that most test-takers
spend too long reading the passage. Then, they try to
answer the questions by memory. So, ETS creates a lot of
wrong answers by simply recycling memorable words and
phrases back into the answer choices. These answers are
very appealing because you’ll remember reading something
like that. But, the correct answer is usually a paraphrase of
the information in the passage. Just remember that the more
that an answer sounds like it is word for word from the
passage, the less likely it is to be right. So be suspicious of
answers that make you say “Wait! I remember reading
that!”
c.
Half Right = All Wrong. ETS likes to write answer
choices that are half right; which also means they’re half—
and thus all—wrong. The first part of the answer choice
will usually look good, but the second part will be incorrect.
Make sure to read the entire choice carefully.
d.
Bad Comparisons. Be suspicious of answers that contain
comparison words such as more…than, less…than, greater,
faster, compared to, etc. In most cases, the items in the
answer choice are mentioned in the passage but they aren’t
compared in the passage. So, always be wary of answers
that make comparisons. If you can’t find the comparison in
the passage, cross the answer off.
Correct answers are paraphrases of information stated in the passage.
Let’s try a fetch question with the short passage you saw before.
Prior to 1735, there was no legal precedent for freedom of the press. The
constitutional concept of freedom of the press traces its origins to 1735 and the
libel trial of John Peter Zenger. Zenger, born in Germany, emigrated to
America in 1710 and established The New York Weekly Journal in 1733. The
Journal starkly opposed the policies of New York governor William Cosby and
while Zenger did not write the majority of the critical pieces, he was arrested
on libel charges in 1734. In the ensuing trial, widely followed by the populace,
Zenger was defended by Andrew Hamilton, a Pennsylvania lawyer who was
brought in after Cosby disbarred all the New York lawyers who offered to
defend Zenger. Hamilton’s brilliant defense of Zenger was predicated on the
argument that since Zenger’s criticisms involved verifiable facts, they could
not possibly be considered libel. The judge agreed and acquitted the publisher,
establishing the basic concept of freedom of the press that was to be enshrined
in the United States Constitution some 57 years later.
And here’s the question:
The passage states that Zenger did all of the following EXCEPT
started his own newspaper
opposed the governor’s administration
left his homeland to come to the United States
sought out Andrew Hamilton to defend him
based his criticisms on factual issues
Always go back to the
passage to verify your
answer. Don’t answer
from memory.
Here’s How to Crack It
Step 1:
Read the Question. Essentially, “What did Zenger do?” This is a
fetch question.
Step 2:
Make the Question Back into a Question. What did Zenger do?
Step 3:
Find Proof. “Zenger” will make a nice lead word. Find the first
instance of it in the passage and read from five lines above to five
lines below.
Step 4:
Link the Info in the Passage to the Question Task. In the
passage, we are told that Zenger “emigrated to America,”
“established The New York Weekly Journal,” and “opposed the
policies of New York governor William Cosby.”
Step 5:
Use Process of Elimination. Use your scratch paper. Cross off
(A), (B), and (C). Now we need more information, so go back to
the passage and find more instances of the lead word Zenger. We
are told that he “was defended by Andrew Hamilton” and that his
“criticisms involved verifiable facts.” Choice (D) says that Zenger
“sought out Andrew Hamilton to defend him.” One might assume
that since Hamilton defended him, Zenger must have sought
Hamilton out to do so. Be careful, and be literal. This is how they
catch smart people. If you cannot prove your answer with
something stated in the passage, you can’t pick it. If the passage
doesn’t say Zenger sought out Hamilton, we can’t assume it.
Assumptions always get you into trouble on reading comp. If
you’re not convinced, don’t get hung up; just give (D) the maybe,
and move on. Choice (E) says that he “based his criticisms on
factual issues.” We have proof for this one, so cross it off. Choice
(D) is the only one left. That must be our answer.
Don’t get hung up on an
answer choice in the first
pass, and be incredibly
literal. If the passage
doesn’t say it, you can’t
pick it.
Let’s try another fetch question. Try the next question, again based on the
passage we’ve already studied:
Which of the following would most effectively replace the phrase predicated on as
it is used in the passage?
derived from
extirpated on
conjectured on
covenanted on
relegated to
Here’s How to Crack It
Treat this type of question just like a Text Completion problem. Go back to
the passage and read the sentence that contains the highlighted phrase,
imagining that the highlighted portion is missing: “Hamilton’s brilliant
defense of Zenger was ____________ the argument that since Zenger’s
criticisms involved verifiable facts, they could not possibly be considered
libel.” Try to come up with your own word or phrase for the blank.
The clue is that the defense had something to do with the “argument that
was….” A good phrase might be based on or constructed on. Now go to the
answer choices and use POE. Does derived from mean based on? It’s fairly
close, so leave this choice. How about extirpated? Remember that if you’re
not sure of the meaning of this word, you can’t eliminate it. Leave it for now.
Choice (C) is not a match; conjectured means to guess or infer. A covenant is
an agreement, so (D) doesn’t make sense either. And relegate means to
assign, so that’s out too. If you’re down to (A) and (B), go with the one you
know works. Choice (A) definitely works, so that’s our answer.
By the way, to extirpate means to tear up by the roots or destroy completely.
Remember to keep track
of new vocabulary
words as you work
through this book!
Select-in-Passage Questions
Think of these as regular fetch questions, but the answer choices are in the
passage rather than part of the question. Most of the time you will find these
questions on short passages, but should they occur on a long passage, ETS
will limit the scope of the question to a single paragraph. Follow the same
steps as you would on a fetch question. Put the question into your own words.
Anticipate the answer; then select it from the five or six sentences in the
paragraph or passage.
Here’s a practice Select-in-Passage question:
Prior to 1735, there was no legal precedent for freedom of the press. The
constitutional concept of freedom of the press traces its origins to 1735 and the
libel trial of John Peter Zenger. Zenger, born in Germany, emigrated to
America in 1710 and established The New York Weekly Journal in 1733. The
Journal starkly opposed the policies of New York governor William Cosby and
while Zenger did not write the majority of the critical pieces, he was arrested
on libel charges in 1734. In the ensuing trial, widely followed by the populace,
Zenger was defended by Andrew Hamilton, a Pennsylvania lawyer who was
brought in after Cosby disbarred all the New York lawyers who offered to
defend Zenger. Hamilton’s brilliant defense of Zenger was predicated on the
argument that since Zenger’s criticisms involved verifiable facts, they could
not possibly be considered libel. The judge agreed and acquitted the publisher,
establishing the basic concept of freedom of the press that was to be enshrined
in the United States Constitution some 57 years later.
Select the sentence in which the author offers an opinion.
Here’s How to Crack It
Select the sentence in which the author offers an opinion.
First, read the question and summarize it in your own words. The question is
looking for an opinion, as opposed to a fact, and specifically, the author’s
opinion. Note that there are actually only seven sentences in this passage, so
you have seven answer choices. One of them must contain an opinion. The
other six, therefore, must be factual. This is a great case for POE. Write (A),
(B), (C), (D), (E), (F), and (G) on your scratch paper so you have something
to eliminate.
Sentences 1 and 2—All dates and facts. Cross off (A) and (B).
Sentence 3—More facts. Cross off (C).
Sentence 4—More facts. Cross off (D).
Sentence 5—More facts. Cross off (E).
Sentence 6—The author describes Hamilton’s defense as “brilliant.” This is
an opinion, not a fact. This is a possible answer. Give it a check.
Sentence 7—More facts. Cross off (G). The correct answer is sentence 6.
Now that we’ve cracked the fetch questions, let’s move onto the next major
type: reasoning questions.
Reasoning Questions
Reasoning questions ask us to do a little more work to find the proof in the
passage. The best answer is still based on the passage, but we need to do extra
work to get it. Our steps for reasoning questions are pretty similar to those for
fetch questions:
1. Figure Out What the Question Wants. Reasoning questions
never ask for a simple fact from the passage. Instead, you’ll need to
figure out what type of information the question requires before
you go back to the passage. For example, some reasoning questions
may ask why an author brings up an example. Why do authors ever
bring up examples? Well, to support a point that they either just
made or are about to make. So, you need to find the point that the
author uses the example to support.
2. Return to the Passage. You’ll still need to return to the passage to
find the answer. In general, reasoning questions will require you to
read more of the passage than simple fetch questions because often
you’ll need to know the context for a particular piece of
information.
3. Answer in Your Own Words If Possible. You’ll be able to
complete this step for some reasoning questions, but not for others.
If you can’t answer in your words, go right to the answers and use
POE.
POE Guidelines for Reasoning Questions
On many reasoning questions you’ll have to make aggressive use of POE.
Much of the guidelines you used for fetch questions still apply. However, on
reasoning questions, look out for answer choices that do the following:
1. Go Beyond the Information Given Often, wrong answers on
these questions will go beyond the scope of the passage. In most
cases, the wrong answer simply makes a claim that is stronger than
the claim in the passage. In other words, be on the look out for
extreme language! Choose the answer that is closest to the
information in the passage.
2. Have the Wrong Tone Some reasoning questions, such as
strengthen and weaken questions, can use extreme language while
others, such as inference questions, generally should not. Make
sure the tone of the answer choice is appropriate to the question
task.
3. Are Only Half Right Again, answers that are only half right are all
wrong and you should eliminate them.
Here’s a practice reasoning question and another familiar passage to work
with:
What was it about Oscar Wilde’s only novel, The Picture of Dorian Gray,
that caused it to create such an uproar when it was published in 1891? While
critics attacked the quality of Wilde’s work, lambasting its plot as “incurably
silly” and chiding the writer for using prose that was “clumsy” and “boring,”
these overt denunciations of the formal elements of Wilde’s work merely
masked the true concerns of many nineteenth-century critics. What these
critics were actually railing against was the thematic content of Wilde’s work,
specifically his illustration of a lifestyle devoted to useless beauty. For many a
nineteenth-century moralist, The Picture of Dorian Gray was nothing more
than a primer for spiritual depravity. Wilde’s ultimate sin was not his clunky
plot or his sometimes cloying prose; it wasn’t even his disregard for the timehonored tradition of English propriety. It was instead his leniency toward his
protagonist. Wilde propagated the disdain of critics not simply because Dorian
Gray was an unabashed hedonist, but because Wilde failed to punish his
subject appropriately for his hedonism. To the critics, allowing an evil
character to escape his just desserts was an unforgivable sin, and it was this
transgression that resulted in such opprobrium for Wilde’s work. In their mind,
Wilde’s work was corrupting the genteel reading public by failing to show the
proper consequences of immoral behavior.
The author of the passage would probably consider which one of the following
situations most analogous to the response of the critics in the highlighted sentence?
A college professor lowers a student’s grade from an A to a B because the
student is chronically late to class.
An accountant refuses to help his clients cheat on their income tax returns.
A politician attacks the character of his opponent even though it is his
opponent’s positions that the politician disagrees with.
A district attorney indicts a person on a misdemeanor charge because he
lacks the evidence to convict the person on a felony charge.
A reporter files a story despite not having been able to verify all her sources.
What sort of information
do we need from the
passage in order to
answer this question?
Here’s How to Crack It
This question wants us to figure out what the response of the critics is and
then find a situation that is similar to it. First, return to the passage and read
the highlighted sentence. Based on the sentence, it appears that the situation is
that “the people attacked this thing for one reason, but there was really
another reason they didn’t like it.”
Now you’re ready to return to the answer choices and look for the best match.
The situation in the first answer choice is not the same as what we’ve written;
here the professor is penalizing a student for the student’s poor performance
in class. Eliminate it. Choice (B) doesn’t match—the accountant is refusing to
do something illegal. The third choice seems like a good match; the politician
attacks his opponent for one reason (his character), but there was another
reason (his policies) for his dislike of the candidate.
Let’s check the remaining choices to make sure our answer is the best answer.
In (D), the district attorney indicts on a lesser charge because of a lack of
evidence for a more serious charge. This is somewhat similar, in that there is
an overt element (the misdemeanor charge) and also a second factor which is
not overt (the felony charge). However, the part of the answer choice that
mentions the lack of evidence makes this choice worse than (C). It goes
beyond the information presented in the passage because the original situation
in the passage doesn’t mention a lack of evidence on behalf of the critics.
Finally, (E) is not a match at all. This situation involves a reporter who puts
forth something that has not been verified, which isn’t the same as criticizing
something for one reason when there is another, deeper reason. Thus, (C) is
our answer.
Ready for another reasoning question? It’s based on the passage we just used.
Consider each of the choices separately and select all that apply.
The author of the passage would probably agree with which of the following
statements?
Most critics of Oscar Wilde’s novel objected primarily to the lifestyle of its
author.
If The Picture of Dorian Gray were written in the twenty-first century, the
critical reaction would be less severe.
Some critics of Wilde’s The Picture of Dorian Gray believed that an author of
a book had a moral responsibility to the book’s audience.
Here’s How to Crack It
To answer this question, we have to figure out which answer choice the
author might agree with. How the heck are we supposed to know what the
author might think? Well, all we know about what the author thinks is what’s
found in the passage. In many ways, “author-agree” questions are very similar
to inference questions. In both types of questions, the correct answer may not
be explicitly stated in the passage, but there will be sufficient evidence in the
passage to support the correct answer. The key here is to take each answer
choice one by one and return to the passage to look for proof for it.
On Select All That Apply
questions, don’t feel
compelled to choose more
than one answer—sometimes
only one choice will
be correct!
The first choice states that most critics objected to Wilde’s lifestyle. Can you
find any evidence of this in the passage? No. Nowhere does the passage
mention his lifestyle. It says that the critics disagreed with the thematic
content, but we can’t assume that Wilde based his work on his own lifestyle
(and of course, you can’t use any outside knowledge you may have of Wilde’s
licentious life). Remember: You have to stay inside the scope of the passage
—don’t go beyond the information given. Thus, (A) is no good.
Now look at the second choice. Is there any evidence about how the author
would feel if the book were released today? Nope. Of course, you may
assume that the author would agree with this choice, but again, on the GRE
that isn’t good enough. We need direct evidence from the passage and there is
none for this choice. So, goodbye to (B). Let’s go to the third and final
answer. Return to the passage and look for the part about the book’s audience.
The last two lines make it clear that some critics saw Wilde’s book as
corrupting the public and for this they attacked it. This would support (C), so
(C) is the answer. Notice that in these multiple-choice, multiple-answer
questions, there need not be two answers—sometimes there will just be one!
FIND THE PARAPHRASE OF THE TEXT
Because the right answer to every Reading Comprehension question is
literally right in front of you, ETS goes to great lengths to disguise the correct
answer and to make the wrong answers more appealing. ETS does this by
making the answer a clever paraphrase of the words in the text, one that
basically states the same idea but usually avoids repeating words verbatim
from the text. By paraphrasing, ETS is able to create right answers that “fly
under the radar”; they don’t stand out and they’re easy to dismiss in favor of
the trap answers.
Paraphrasing the information in the text is ETS’s job. Your job is simpler. You
just need to find the information in the passage that addresses the task of the
question. Once you’ve found that information, you can compare each answer
choice to your proof from the passage. If the answer choice is a good
paraphrase of your proof from the passage, then that will very likely turn out
to be the credited response.
As always, balance looking for the right answer with being suspicious of
every answer. For most reading questions, there are more wrong answers than
right answers. So, read each answer choice as though it is likely to be wrong.
USE PROCESS OF ELIMINATION
As you’ve surely noticed by now, the answer to a Reading Comprehension
question is the one that is supported by evidence from the passage. Regardless
of the question type or format, that rule is immutable. Here is a recap of other
guidelines to use when you’re using POE.
1. Avoid Extreme Statements. ETS prefers wishy-washy statements
to extreme ones. When in doubt, pick the answer that has a weaker
tone.
2. Half Right = All Wrong. ETS likes to write answer choices that
are half right; which also means that they’re half—and thus all—
wrong. The first part of the answer choice will usually look good,
but the second part will be incorrect. Make sure to read the entire
choice carefully.
3. Recycled Language. Some wrong answer choices just take parts of
the passage and garble them. These answers usually contain
information that’s taken directly from the passage rather than
paraphrasing it. Eliminate them!
4. Beyond the Information Given. These answers go too far beyond
what is written in the passage. If you can’t point to a part of the
passage that matches information in the answer choice, that choice
is probably wrong.
Let’s explore these guidelines in a little more detail.
ETS constructs correct
answer choices that
cannot be disputed. The
more extreme a choice is,
the less likely it is to be
the answer.
Avoid Extreme Statements
Extreme statements are answer choices that make absolute claims. There are
very few absolutes in the world, so you shouldn’t expect ETS reading
passages (which are all excerpted or based on actual academic papers) to
contain extreme statements.
Certain words make choices extreme and, therefore, easy to dispute. Here are
a few of these words.
•
must
•
the first
•
each
•
every
•
all
•
the best
•
only
•
totally
•
always
•
no
Extreme answers
are bad!
You shouldn’t automatically eliminate a choice that contains one of these
words, but you should turn your attention to it immediately and attack it
vigorously. If you can find even one exception, you can eliminate that choice.
Other words make choices moderate, more mushy, and therefore hard to
dispute. Here are a few of these words.
•
may
•
can
•
some
•
many
•
sometimes
•
often
Moderate answers
are good!
For example, consider the following two answer choices:
There is assuredly life on other planets or moons in the solar system.
Scientists believe that there may be life on other planets or moons in the
solar system.
Without even looking at a passage, you should pick the second answer choice
because it’s more wishy-washy; the first choice is too strong for ETS’s liking.
Half Right = All Wrong
Careful reading of the answer choices is essential on Reading Comprehension
questions. Remember that your job is to find flaws in answer choices and
eliminate them. Many people focus on what they like about an answer, rather
than what’s wrong with it. ETS loves to write answer choices that start out
fine, but then say something wrong. Don’t be taken in by the part of the
answer you like. Use a critical eye when applying POE; don’t look for
reasons to keep disputed answer choices, look for reasons to eliminate them.
One word can make an answer choice wrong if that word isn’t supported by
the passage.
If an answer choice is
half wrong, it’s all wrong.
Focus on flaws and use
Process of Elimination.
Look at the following example for the next three example questions:
Within the atmosphere are small amounts of a number of important gases,
popularly called “greenhouse gases,” because they alter the flow of life- and
heat-energy through the atmosphere, much as does the glass shell of a
greenhouse. Their effect on incoming solar energy is minimal, but collectively
they act as an insulating blanket around the planet. By absorbing and returning
to the earth’s surface much of its outgoing heat, these gases trap it within the
lower atmosphere. A greenhouse effect is natural and essential to a livable
climate on Earth.
The passage states which of the following about the effect of greenhouse gases on
the environment?
Although their effect on incoming solar energy is minimal, the presence of
artificial greenhouse gases is a danger to the planet.
The composite effect of the gases is necessary for maintaining a climate
favorable to life on Earth.
In this case, the first answer starts out great—the passage does indeed state
that the gases have a minimal effect on solar energy. But look at the rest of the
passage. Does the passage ever talk about artificial greenhouse gases? Nope,
so the first answer is half right, but all wrong. The second choice, however, is
entirely supported by the passage. The second sentence states that collectively
they act, while the final sentence says the greenhouse effect is essential to a
livable climate on Earth.
Recycled Language
One of ETS’s favorite tricks is to write answer choices that contain
information from different parts of the passage than the one to which the
question refers. If you aren’t being careful, you’ll think, “I remember
something like that from the passage” and pick the wrong answer choice. This
is one reason it’s so important to use lead words and line references to guide
you to the right part of the passage. Never answer a question from memory.
ETS also likes to conflate different parts of a passage to create an answer that
uses a lot of words from the passage, but doesn’t say a whole lot. For
example, use the passage from the previous section to answer the following
question.
The passage suggests which of the following about “greenhouse gases”?
They are a natural source of heat energy within the atmosphere.
They contribute to creating a habitable environment on Earth.
The first answer choice uses a lot of words from the passage, but says a whole
lot of nothing. It garbles the information in the passage, which states that
greenhouse gases alter heat energy. They are not a source of it. The second
choice, which is the correct choice, is a nice paraphrase of the last sentence. It
may not sound as “correct” as the other choice, but close examination shows
it to be the better answer.
Beyond the Information Given
ETS takes its reading passages from textbooks, collections of essays, works of
scholarship, and other sources of serious reading matter. However, be careful
not to answer questions based on the fact that you did your undergraduate
thesis on the topic, or that you once read a newspaper article about the topic at
hand. The answers are in the passage; don’t use outside knowledge.
Remember: All of the
answers you need
are on the screen.
Often, these answers will make common sense, but unfortunately you can’t
use that as a criterion on the GRE. Which of the following answer choices is
beyond the information in the passage from before?
The author of the passage would probably agree with which of the following
statements?
Without the presence of greenhouse gases, it is unlikely that the earth would
be able to support life.
Air pollution may contribute to an increase in greenhouse gases, which will
in turn lead to eventual warming of the earth.
Clearly, here the second choice is beyond the information given in the
passage. It may be true and it makes common sense, but the passage never
addresses it. Thus, it cannot be the correct answer on a GRE Reading
Comprehension question.
UNDERSTANDING STRUCTURE IN READING
AND WRITING
While the reading passages on the GRE may not represent some of the most
engaging writing you’ve encountered, it is important to keep in mind the
author’s basic goal. Nonfiction writers want their writing to be understood; if
you can’t follow their arguments or their progression of ideas, they’ve failed
in their jobs as writers. When you’re reading or skimming a passage on the
GRE, a good grasp of the structural elements in writing will aid your
understanding.
First, pay attention to the structure of each paragraph. The most important
information is probably going to be found at the beginning and end of the
paragraph. While reading a passage, if your eyes start to glaze over, rest
assured you’re not the only one. Good authors know this and make sure to put
key points where they are likely to stand out. So, focus on the beginning and
end of each paragraph.
Second, look for transition words. Writers use these words as signposts to
direct your reading. When you see same-direction transitions such as for
example, in addition, and, or furthermore, you know the author is going to be
supporting an earlier statement. If you already understand the point of the
paragraph, feel free to skim through these lines. However, change-direction
transitions like although, but, yet, and however, signify an important shift.
Writers use words like this to direct the reader’s attention to an important
change or revelation in the progression of ideas.
Finally, the conclusion of the piece offers the author one last chance to get his
or her point across. Always read the last paragraph. Does the piece wrap
things up nicely or is there some doubt? Does the author suggest further
avenues of inquiry? The way the passage ends can help you to understand the
author’s main point or primary purpose in writing the passage.
Paying attention to structural clues like the ones mentioned here can help you
be a more effective reader. Following these principles in your own writing
wouldn’t hurt either.
Reading Comprehension Drill
Answers can be found in Part V.
Questions 1 through 4 are based on the following reading passage.
Called by some the “island that time forgot,” Madagascar is home to a vast array of unique, exotic
creatures. One such animal is the aye-aye. First described by western science in 1782, it was initially
categorized as a member of the order Rodentia. Further research then revealed that it was more closely
related to the lemur, a member of the primate order. Since the aye-aye is so different from its fellow
primates, however, it was given its own family: Daubentoniidae. The aye-aye has been listed as an
endangered species and, as a result, the government of Madagascar has designated an island off the
northeastern coast of Madagascar as a protected reserve for aye-ayes and other wildlife.
Long before Western science became enthralled with this nocturnal denizen of Madagascar’s
jungles, the aye-aye had its own reputation with the local people. The aye-aye is perhaps best known for
its large, round eyes and long, extremely thin middle finger. These adaptations are quite sensible,
allowing the aye-aye to see well at night and retrieve grubs, which are one of its primary food sources,
from deep within hollow branches. However, the aye-aye’s striking appearance may end up causing its
extinction. The people of Madagascar believe that the aye-aye is a type of spirit animal, and that its
appearance is an omen of death. Whenever one is sighted, it is immediately killed. When combined with
the loss of large swaths of jungle habitat, this practice may result in the loss of a superb example of
life’s variety.
1 of 10
Based on the information given in the passage, the intended audience would most likely be
visitors to a natural science museum
professors of evolutionary science
a third-grade science class
students of comparative religions
attendees at a world culture symposium
2 of 10
The author’s attitude toward the aye-aye, as represented in the highlighted text, could best be described
as
admiring
mystified
reverent
appalled
lachrymose
3 of 10
Select the sentence in the first paragraph that suggests the author’s claim that “this practice may result in
the loss of a superb example of life’s variety” is unlikely to happen.
4 of 10
Consider each of the choices separately and select all that apply.
Which of the following statements can be logically inferred from the passage?
Taxonomic classifications are not always absolute.
The traditional religion of Madagascar involves augury.
There are no longer enough resources on the main island to support the ayeaye population.
Questions 5 through 6 are based on the following reading passage.
A novel that is a bestseller is often, because of its popularity, not taken seriously as literature.
Critics seem to presuppose that great literature must be somehow burdensome to the reader; it must be
difficult for the uninitiated to understand. It is precisely this inverted snobbery that has hindered Isabel
Allende’s The House of the Spirits from gaining the critical attention it deserves.
Published in 1982, the novel draws deeply on the author’s own family history. Allende is the first
cousin once removed of former Chilean president Salvador Allende, who was murdered during a rightwing military coup in 1973. Yet rather than the to-be-expected socialist harangue, Allende subtly works
her political message within the fabric of the compelling narrative she weaves. While Allende borrows a
bit too freely from Gabriel García Márquez’s work, she nevertheless has a powerful and original voice
within the construct of magical realism.
5 of 10
The author of the passage would probably consider which of the following situations to be most
analogous to the critics’ viewpoint as it is described in the highlighted sentence?
Avant-garde movies with complicated storylines are deemed
cinematically superior works to Hollywood blockbusters with
straightforward narratives.
Scientific journals are thought of as providing coverage of natural events
that is inferior to that provided by nature documentaries.
Poetry is considered superior literature to prose because it is shorter, and
therefore the message it conveys is more easily understood.
Political diatribes are viewed as falling outside the accepted literary
canon because they are too controversial.
A movie version of a popular novel is considered artistically superior to
the original.
6 of 10
It can be inferred from the passage that
Allende’s novel is a retelling of her family’s political struggles
Allende’s novel would have received more favorable reviews if critics
had believed it to be great literature
Allende learned about magical realism from Gabriel García Márquez
Allende’s novel could have been more compelling if she had included a
stronger political message
readers might have expected Allende’s work to be more political than it
actually was
Questions 7 through 8 are based on the following reading passage.
Bronson Alcott is perhaps best known not for who he was, but for whom he knew. Indeed, Alcott’s
connections were impressive by any standards: He was a close confidante of such luminaries as
Margaret Fuller, Ralph Waldo Emerson, and Henry David Thoreau. Yet, to remember the man solely by
his associations is to miss his importance to nineteenth-century American philosophy as a whole and to
the Transcendental Movement in particular. Admittedly, Alcott’s gift was not as a writer. His
philosophical treatises have rightly been criticized by many as being ponderous, esoteric, and lacking
focus.
However, Alcott was an erudite orator, and it is in the text of his orations that one begins to
appreciate him as a visionary. Most notably, Alcott advocated what were at the time polemical ideas on
education. He believed that good teaching should be Socratic in nature and that a student’s intellectual
growth was concomitant with his or her spiritual growth.
7 of 10
It can be inferred from the passage that the author would agree with all of the following statements
EXCEPT
Alcott should be remembered for his contributions to Transcendentalism
Alcott’s ideas were ahead of those of many of his contemporaries
Alcott believed that learning should not neglect a student’s spiritual
education
Alcott’s ideas about education were not always accepted by his
compatriots
Alcott should not be regarded as a particularly gifted orator
8 of 10
It can be inferred that the author would agree with which of the following statements?
Transcendentalism was an esoteric field of inquiry promulgated by a
select group of visionaries.
Alcott’s prose style is not always easily understood.
A Socratic pedagogical style is difficult to align with spiritual teaching.
Alcott should be chiefly appreciated for the strengths of his association.
The text of Alcott’s orations were widely accepted by his peers.
Questions 9 through 10 are based on the following reading passage.
Echinosorex gymnura, known colloquially as the moonrat or gymnure, is one of the many
fascinating creatures that inhabit the jungles of Southeast Asia. A close relative of the hedgehog, the
moonrat likewise belongs to the order Insectivora and the family Erinaceidae. However, the family then
splits into the sub-family Hylomyinae, which contains three separate genera and eight distinct species.
The appearance and habitat of the moonrat are actually far more similar to those of various members of
the order Rodentia, though its eating habits are more in line with its fellow insectivores. Ultimately, the
taxonomic classification of this animal is useful only when considered along with other information
regarding the animal’s ecological niche.
9 of 10
Consider each of the choices separately and select all that apply.
Which of the following scenarios demonstrates the idea put forth by the author of this passage regarding
animal classification?
While studying a population of bears, scientists rely solely on the
traditional taxonomic designations to identify likely hunting grounds.
A team of medical researchers closely monitors the actions of the
animals involved in a study and compares its findings with prevailing
beliefs about those animals.
A zookeeper designs a habitat for a new acquisition, disregards
taxonomic classifications and instead focuses on observational data.
10 of 10
The author’s tone could best be described as
exasperated
didactic
ambivalent
morose
laudatory
Summary
Before answering the questions, attack the passage. Read the passages
looking for the main idea, structure, and tone. Remember that looking
for problems or changes is the key to finding the main idea.
For short passages, read the entire passage. For medium passages, focus
on the beginning and end. For longer passages, read the first few lines
of each paragraph and the final lines of the entire passage.
Take a moment to understand the question task. Fetch questions ask
you to retrieve information from the passage. Reasoning questions ask
you to do something more than simply figure out what the author is
saying.
Return to the passage to find the answer to the question. Don’t answer
from memory! Go back to the text and find the answer.
Try to come up with an answer in your own words before looking at the
answer choices ETS provides. Remember to look for paraphrases of the
text, not direct quotes.
Eliminate answers that contain extreme language, go beyond the
information provided, garble the meaning of the text, or otherwise have
information that you can’t support from the text.
Chapter 7
Critical Reasoning
While ETS considers Critical Reasoning questions to fall within the category
of Reading Comprehension questions, the questions are different enough to
merit a separate discussion. Let’s jump in!
CRITICAL REASONING
Critical Reasoning questions are composed of short reading passages,
typically just one paragraph long, followed by a series of questions about the
author’s argument. You should expect to see anywhere from two to four
Critical Reasoning questions within the two GRE Verbal sections.
Here’s a sample Critical Reasoning passage and question:
For more than fifty years, many evolutionary biologists posited that early fish such
as Eusthenopteron developed limbs as a result of the need to drag themselves
across short distances when their watery habitats dried up during periods of
drought. However, new fossil evidence suggests that this hypothesis is incorrect.
Fossilized remains of Acanthostega, a primitive fish, reveal that even though the
animal had rudimentary limbs, it could not walk on land. Acanthostega lacked
ankles, which means that its limbs couldn’t support its weight; furthermore, its ribs
were too short to prevent the organism’s chest cavity from collapsing once the
animal left water.
Which of the following would most strengthen the author’s argument?
The fossilized remains of the Acanthostega are the earliest known evidence of
early fish.
The modern descendants of Acanthostega are not able to drag themselves
across short distances on land.
Biologists have found that some aquatic species can successfully drag
themselves across land even though these species do not possess ankles.
Any animal with a collapsed chest cavity is not able to survive long enough to
travel even a short distance across land.
Some evolutionary biologists believe that the new fossils are not from
Acanthostega.
The answer to this
question, by the way, is
(D). Not sure why?
Keep reading.
What Exactly Is Critical Reasoning?
Critical reasoning is our term for a specific type of reading passage you’ll
encounter on the GRE. At first glance, Critical Reasoning passages resemble
the short Reading Comprehension passages. However, what distinguishes
critical reasoning from a regular reading comprehension passage is twofold:
1. The structure of the passage
2. The types of questions ETS will ask about it
We’ll show you how to identify Critical Reasoning passages and the most
effective way of tackling these questions as well.
BREAKING AN ARGUMENT DOWN
The key to doing well on Critical Reasoning questions is understanding how
ETS authors construct an argument. All arguments contain two major parts—
the conclusion, or the main point of the argument, and the premise—the facts
that the author gives in support of his or her conclusion. Identifying these two
parts is crucial to your success on these questions. Let’s start our analysis of
an author’s argument in a Critical Reasoning passage by learning how to
identify the conclusion.
Identifying the Conclusion
The conclusion is the most important part of the argument; quite simply, it is
the reason the argument exists. The conclusion of an argument is generally a
statement of opinion—it’s the author’s belief or prediction about a situation.
Let’s look at the sample Critical Reasoning passage again:
For more than fifty years, many evolutionary biologists posited that early fish such
as Eusthenopteron developed limbs as a result of the need to drag themselves
across short distances when their watery habitats dried up during periods of
drought. However, new fossil evidence suggests that this hypothesis is incorrect.
Fossilized remains of Acanthostega, a primitive fish, reveal that even though the
animal had rudimentary limbs, it could not walk on land. Acanthostega lacked
ankles, which means that its limbs couldn’t support its weight; furthermore, its ribs
were too short to prevent the organism’s chest cavity from collapsing once the
animal left water.
You can identify the conclusion of the author’s argument by asking yourself
this question: What opinion does this author hold? Now underline the
sentence that you think is the conclusion of the argument above.
The conclusion is the
author’s main point.
If you underlined “new fossil evidence suggests that this hypothesis is
incorrect,” you hit the nail on the head.
There are other ways of identifying conclusions in arguments. For example,
often you can identify the conclusion by certain key words. Specifically, keep
an eye out for the following:
therefore
thus
consequently
and so
in conclusion
You should also look for any words that indicate an opinion, such as the
following:
suggest
believe
hope
indicate
argue
follow
In addition, a conclusion is often a belief about what should or might happen.
Look for the following:
should
would
must
will
Remember: The
conclusion is often the
author’s opinion about
what might happen.
Practice: Identifying Conclusions
Underline the conclusions of the arguments in the following Critical
Reasoning passages. Answers can be found in Part V.
1 of 5
Despite the support of the president, it is unlikely that the new defense bill will pass. A bipartisan group
of 15 senators has announced that it does not support the legislation.
2 of 5
The earliest known grass fossils date from approximately 55 million years ago. Dinosaurs most likely
disappeared from the earth around 60 million years ago. Based on this evidence, as well as fossilized
remains of dinosaur teeth that indicate the creatures were more suited to eating ferns and palms,
scientists have concluded that grass was not a significant part of the dinosaur diet.
3 of 5
Automaker X has lost over 2 billion dollars this year due to rising costs, declining automobile sales, and
new governmental regulations. Because of the company’s poor financial situation, it has asked its
employees to pay more for health care and to accept a pay cut. However, the workers at automaker X are
threatening to go on strike. If that happens, automaker X will have no choice but to file for bankruptcy.
4 of 5
The rise of obesity among citizens of country Y has been linked to a variety of health problems. In
response to this situation, the country’s largest health organization has called for food manufacturers to
help combat the problem. Since the leading members of the nation’s food industry have agreed to
provide healthier alternatives, reduce sugar and fat content, and reduce advertisements for unhealthy
foods, it is likely that country Y will experience a decrease in obesity-related health problems.
5 of 5
Recent advances in technology have led to a new wave of “smart” appliances, including refrigerators
that note when food supplies are low and place an order at the grocery store, washing machines that
automatically adjust the wash cycle and temperature based upon the clothes in the machine, and
doorknobs that can identify the house owner and automatically open the door. A technology expert
predicts that, due to these new innovations, machines will soon outnumber humans as the number-one
users of the Internet.
Some Critical Reasoning questions ask you to find the conclusion of the
argument. Here’s an example:
Mutation breeding is a method of crop development that requires breeders to first
find plants that randomly display the traits researchers are looking for, and then
breed those plants with other plants displaying similar traits. In order to bring about
the required mutations, researchers bombard plants with thermal neutrons, x-rays,
and known carcinogenic chemicals in order to damage the plant’s DNA. Today,
almost all varieties of wheat grown commercially are products of mutation
breeding. Ironically, when scientists discovered how to splice desirable genes
directly into the plants, thus avoiding the use of harmful chemicals and radiation,
critics derided the new process as potentially dangerous despite the lack of any
supporting evidence, resulting in boycotts and bans on genetically modified foods.
The argument as a whole is structured to lead to which of the following
conclusions?
Genetically modified food may have been unfairly stigmatized by its critics.
Mutation breeding produces safer food than does genetic modification.
Foods produced by genetic modification are healthier than foods produced
by mutation breeding.
Researchers should stop using mutation breeding in order to modify foods.
Genetic modification of plants is more cost effective than mutation breeding
of plants.
Here’s How to Crack It
The conclusion, as you’ll recall, is the author’s opinion or belief. As you read
the argument, look for indicators of the author’s opinion. The first three
sentences of the argument do not state opinions; the author is simply
describing the method of mutation breeding. However, in the fourth sentence,
the author uses the word ironically. This is an indicator of how the author
feels. The author believes it is ironic that genetically modified foods are
banned, despite any supporting evidence that they are dangerous, while foods
created with mutation breeding, which use harmful chemicals and radiation
account for almost all varieties of wheat.
Now we just need to find an answer choice that matches this opinion. Choice
(A) looks pretty close, so let’s hang on to it. Choice (B) is the opposite of
what the author argues; the argument implies that genetic modification is
safer. Choice (C) is close, but the argument doesn’t really discuss which foods
are “healthier,” just that one type is banned and the other type isn’t. Choice
(D) also isn’t discussed. The author thinks it’s ironic that genetically modified
foods are banned, but never states that mutation breeding should be stopped.
Finally, (E) doesn’t work because the argument doesn’t express any opinion
about cost effectiveness. Thus, (A) is correct.
Finding the Premise
After you identify the conclusion of an argument, your next task is to find the
argument’s premise. The premise (or premises—there can be more than one)
is the evidence that the author gives in support of the conclusion.
You can find the premise of an argument in two ways. First, look for
statements of fact. Critical Reasoning passages are usually based on statistics,
surveys, polls, or reports and all of these things are premises—in fact, these
are the most common types of premises. Second, you can use a strategy we
call the “Why?” test. Once you’ve found the conclusion, ask yourself why you
should accept it; the answer or answers to that question will be the premise(s).
Let’s look again at the passage from the beginning of the chapter:
For more than fifty years, many evolutionary biologists posited that early fish such
as Eusthenopteron developed limbs as a result of the need to drag themselves
across short distances when their watery habitats dried up during periods of
drought. However, new fossil evidence suggests that this hypothesis is incorrect.
Fossilized remains of Acanthostega, a primitive fish, reveal that even though the
animal had rudimentary limbs, it could not walk on land. Acanthostega lacked
ankles, which means that its limbs couldn’t support its weight; furthermore, its ribs
were too short to prevent the organism’s chest cavity from collapsing once the
animal left water.
What facts does the author give in support of the conclusion? In this
argument, the author provides the following facts: (1) Acanthostega lacked
ankles, and (2) the creature’s ribs were too short to prevent its chest cavity
from collapsing. These facts are the premises of the argument.
Finally, just like conclusions, premises have certain indicator words.
because
due to
since
based on
Is the statement a fact,
something that you could
verify or prove? Then it’s a
premise.
Practice: Finding the Premise
For each of the following arguments, identify the premise or premises that
support the conclusion. (Remember, you already found the conclusions in the
exercise on this page.) Answers can be found in Part V.
1 of 5
Despite the support of the president, it is unlikely that the new defense bill will pass. A bipartisan group
of 15 senators has announced that it does not support the legislation.
Conclusion:
Why?
Premise:
2 of 5
The earliest known grass fossils date from approximately 55 million years ago. Dinosaurs most likely
disappeared from the earth around 60 million years ago. Based on this evidence, as well as fossilized
remains of dinosaur teeth that indicate the creatures were more suited to eating ferns and palms,
scientists have concluded that grass was not a significant part of the dinosaur diet.
Conclusion:
Why?
Premise:
3 of 5
Automaker X has lost over 2 billion dollars this year due to rising costs, declining automobile sales, and
new governmental regulations. Because of the company’s poor financial situation, it has asked its
employees to pay more for health care and to accept a pay cut. However, the workers at automaker X are
threatening to go on strike. If that happens, automaker X will have no choice but to file for bankruptcy.
Conclusion:
Why?
Premise:
4 of 5
The rise of obesity among citizens of country Y has been linked to a variety of health problems. In
response to this situation, the country’s largest health organization has called for food manufacturers to
help combat the problem. Since the leading members of the nation’s food industry have agreed to
provide healthier alternatives, reduce sugar and fat content, and reduce advertisements for unhealthy
foods, it is likely that country Y will experience a decrease in obesity-related health problems.
Conclusion:
Why?
Premise:
5 of 5
Recent advances in technology have led to a new wave of “smart” appliances, including refrigerators
that note when food supplies are low and place an order at the grocery store, washing machines that
automatically adjust the wash cycle and temperature based upon the clothes in the machine, and
doorknobs that can identify the house owner and automatically open the door. A technology expert
predicts that, due to these new innovations, machines will soon outnumber humans as the number-one
users of the Internet.
Conclusion:
Why?
Premise:
Okay. So you know how to identify the conclusion and premise(s) of an
argument. Are you ready to try a Critical Reasoning question? Here’s one way
in which ETS will test your knowledge of the parts of an argument.
What’s the conclusion?
What’s the premise?
A common myth is that animals can sense an impending earthquake. And while
most geophysicists dispute this assertion and claim that there is no way to predict
an earthquake, a new hypothesis for predicting earthquakes is generating interest in
the scientific community. This hypothesis is based on a well-known principle:
Subjecting rocks to extreme pressures causes the rocks to produce electrical
currents. Now, a leading physicist has proposed that this principle may help
predict earthquakes. For example, an earthquake along the San Andreas Fault in
California could produce hundreds of thousands of amperes (units of electrical
current) that would disrupt the ionosphere surrounding the earth. By monitoring
the ionosphere for electrical fluctuations, scientists may be able to predict
earthquakes.
In the argument above, the two boldfaced statements play which of the following
roles?
The first statement expresses the conclusion of the argument while the
second statement provides support for that conclusion.
The first statement expresses the conclusion of the argument as a whole; the
second statement provides a possible consequence of the conclusion.
The first statement presents support for the conclusion of the argument as a
whole; the second statement states the conclusion of the argument.
The first statement expresses an intermediary conclusion of the argument
while the second statement presents a possible objection to the intermediary
conclusion.
The first statement provides support for a conclusion that the argument
opposes; the second statement expresses the conclusion that the argument as
a whole opposes.
Here’s How to Crack It
The key to cracking this question is using the “Why?” test. Let’s try using the
“Why?” test on the two boldfaced statements and see which one works best.
If we make the first statement the conclusion, we’d end up with something
like this:
Conclusion: Subjecting rocks to extreme pressures causes the rocks to
produce electrical currents.
Why?
Premise: By monitoring the ionosphere for electrical fluctuations, scientists
may be able to predict earthquakes.
Does that make sense? Nope, so let’s eliminate any answers that say that the
first sentence is the argument’s conclusion. That allows us to eliminate (A),
(B), and (D). Now let’s see what happens if we flip the statements around:
Conclusion: By monitoring the ionosphere for electrical fluctuations,
scientists may be able to predict earthquakes.
Why?
Premise: Subjecting rocks to extreme pressures causes the rocks to produce
electrical currents.
That makes much more sense. Choice (E) states that the argument opposes the
conclusion, which it doesn’t, so we can eliminate that choice. Choice (C) is
the answer.
The “Why?” test helps to identify premises and conclusions.
Locating Assumptions
Although ETS frequently asks Critical Reasoning questions about the premise
or the conclusion of an argument, there are a number of other question types
that require you to work with one final part of an argument. The final part of
an argument is the assumption. The assumption is never explicitly stated in
the passage, which means that it can sometimes be tricky to find. Basically,
the assumption is the missing link that connects the conclusion of an
argument to its premise.
Let’s look back at one of the arguments you’ve already worked on.
Conclusion: It is unlikely that the new defense bill will pass.
Why?
Premise: A bipartisan group of 15 senators has announced that it does not
support the legislation.
In order for this argument to be convincing, the reader has to make an
assumption that because 15 senators do not support the bill, the bill will
probably not pass. If you don’t assume that the opposition of 15 senators
means that the bill is unlikely to pass, the argument fails. Thus, assumptions
are necessary to a successful argument.
To find the assumption or assumptions in an argument, you need to look for a
“gap” in the reasoning of the argument. You can often accomplish this by
asking yourself the following question:
Just because (premise) is true, does it really mean (conclusion) is true?
For example, let’s return to another of the arguments you’ve already tackled.
Conclusion: Country Y will experience a decrease in obesity-related health
problems.
Why?
Premise: The leading members of the nation’s food industry have agreed to
provide healthier alternatives, reduce sugar and fat content, and reduce
advertisements for unhealthy foods.
Now, let’s ask ourselves the question: Just because it’s true that the food
industry has agreed to provide healthier alternatives, reduce sugar and fat
content, and reduce advertisements for unhealthy foods, does it really mean
that obesity-related health problems will decrease?
If you accept this argument, you must assume that the food industry’s actions
will lead to a decrease in obesity-related health problems. That’s the missing
link—or the assumption—required by the argument.
Practice: Locating Assumptions
For each of the following Critical Reasoning questions, identify the
conclusion and the premise. Then note what assumption is required to make
the argument work. Answers can be found in Part V.
1 of 4
City University recently announced the retirement of Professor Jones. Professor Jones is a leading
biologist and widely published author and her presence was a major factor in many students’ decisions
to attend City University. The University predicts no decline in enrollment, however, because it plans to
hire two highly credentialed biology professors to replace Professor Jones.
Conclusion:
Premise:
Assumption:
2 of 4
It is unjust to charge customers under the age of 25 more to rent a car than those over the age of 25.
After all, most states allow people as young as 16 to have a driver’s license and all states allow 18-yearolds the right to vote.
Conclusion:
Premise:
Assumption:
3 of 4
It is easy to demonstrate that extraterrestrial life exists by simply looking at our own solar system. In
our solar system, there are eight planets and at least one of them obviously has life on it. Thus, roughly
12.5% of planets in the universe should have life on them.
Conclusion:
Premise:
Assumption:
4 of 4
State A is facing a serious budget shortfall for the upcoming year. Recent polls indicate that 58% of
voters in Township B approve of a proposed 2-cent gasoline tax in order to make up the deficit. It is
clear, therefore, that the leaders of State A should institute the gas tax.
Conclusion:
Premise:
Assumption:
CRITICAL REASONING QUESTION TYPES
Now that you’ve familiarized yourself with the basics of an argument, let’s
look at the types of argument questions you’ll encounter on the GRE. Each of
the following types of questions will require you to first identify the
argument’s premise and conclusion; after that, your task will vary depending
on the type.
Reasoning Questions
You can identify Reasoning questions because they will have the following
question stems:
In the argument given, the boldfaced statements play which of the following roles?
Which of the following best describes the function of the boldfaced statements in
the argument above?
The argument above is structured to lead to which of the following conclusions?
For Reasoning questions, you must isolate the premise and conclusion, but
you don’t need to find the assumption.
Need More Verbal
Help?
Check out Verbal Workout
for the GRE for additional
verbal review from The
Princeton Review.
Assumption Questions
Assumption questions are usually phrased in the following ways:
The argument above assumes which of the following?
The argument above relies on which of the following?
The author’s argument presupposes which of the following?
On Assumption questions, you need to first locate the premise and
conclusion. After that, look for the gap as described in the “Locating
Assumptions” section above.
Strengthen Questions
Strengthen questions will ask you to make the argument stronger. You’ll be
asked to do this by identifying answer choices that will support the
assumption. Strengthen questions are often phrased as follows:
Which one of the following, if true, would most strengthen the argument?
Which of the following, if true, would most support the author’s argument?
Supporters of the argument would most likely cite which of following pieces of
additional evidence?
To strengthen an argument, find the premise, the conclusion, and the
assumption. The correct answer will be a premise that supports the
assumption.
Weaken Questions
As we’ve learned, the assumption is what makes an argument work. It
follows, then, that if you attack the assumption, you will weaken the
argument. You can identify Weaken questions by looking for the following:
Which one of the following, if true, would most weaken the argument?
Which one of the following, if true, casts the most doubt on the argument above?
Which one of the following, if true, would most undermine the author’s argument?
On Weaken questions, once again you’ll need to find the premise, conclusion,
and assumption. The right answer will attack the assumption, breaking the
link between the premise and the conclusion.
CRACKING CRITICAL REASONING
QUESTIONS
Ready to tackle some Critical Reasoning questions? Let’s go through steps
you take when you run into one of these questions on the test.
The Basic Approach
When you identify a question as a Critical Reasoning question on the exam,
go through the following steps:
1. Read the Question Carefully. Don’t dive into the passage without
being aware of exactly what you’re dealing with—start by making
sure that it really is critical reasoning and not a plain old reading
comprehension passage.
2. Analyze the Argument. Identify the premise, conclusion, and
assumption of the argument.
3. Know What the Answer Needs to Do. For each type of question,
you can know what characteristic the right answer needs. For
example, a Weaken question attacks the assumption of the
argument.
4. Use Process of Elimination. Process of Elimination (POE) is a
valuable tool. If you’re not sure what the correct answer is, look for
the wrong answers instead; eliminate them, and even if you still
can’t identify the correct answer, you have a much greater chance
of guessing the correct answer.
Try going through these steps on the following question.
After examining the bodies of a dozen beached whales and finding evidence of
bleeding around the animals’ eyes and brains as well as lesions on their kidneys
and livers, environmental groups fear that the Navy’s use of sonar is causing
serious harm to marine animals. A leading marine biologist reports that sonar
induces whales to panic and surface too quickly, which causes nitrogen bubbles to
form in their blood.
The argument above relies on which of the following assumptions?
Marine biologists have documented that other marine animals, including
dolphins and sea turtles, have exhibited kidney and liver lesions.
No studies have been conducted on the possible detrimental effects of sonar
on marine animals.
Whales in captivity panic only when exposed to man-made, rather than
natural, sound waves.
The presence of nitrogen bubbles in the blood has been demonstrated to
cause damage to various internal organs.
It is unlikely that the symptoms found in the beached whales could be
caused by any known disease.
What type of
question is this?
Here’s How to Crack It
Let’s apply the four-step basic approach:
1. Read the Question Carefully. This is an Assumption question—
we know this because it asks you to determine what the argument
relies on.
2. Analyze the Argument. Be sure to precisely identify the
conclusion and premise. You should come up with the following:
Conclusion: The Navy’s use of sonar is causing serious harm to
marine animals.
Why?
Premise: Surfacing too quickly causes nitrogen bubbles to form in
the whale’s blood.
Next, we need to locate the assumption. Remember to use the
question we introduced earlier—here it would be phrased as
follows:
“Just because the whales have nitrogen bubbles in their blood, does
that really mean that sonar is causing them serious harm?”
3. Know What the Answer Needs to Do. Assumptions connect the
premise to the conclusion. So, you want an answer that has
something from both the premise and the conclusion in it.
4. Use Process of Elimination. Check out the gray box for some POE
tips on Assumption questions.
Eliminate answers that
aren’t relevant to the
argument!
Now, returning to the answer choices, let’s see which one is best. Choice (A)
is wrong; this choice doesn’t connect the premise to the conclusion. Even
though it states that other animals have exhibited similar symptoms, we need
the answer choice to connect the symptoms—in whales—to the use of sonar.
Choice (B) is wrong as well because it brings in information that isn’t part of
the original argument: It’s irrelevant whether or not the Navy has conducted
studies on the harmful effects of sonar. Choice (C) doesn’t help much either;
the argument is not concerned with the situations under which whales panic.
Choice (D) looks pretty good. It connects the nitrogen bubbles found in the
premise to the serious harm mentioned in the conclusion, so hold on to this
choice. Remember that you always need to check all five answer choices;
however, (E) is no good. Like (B), this choice brings in information that isn’t
relevant to the argument. The fact that the symptoms are unlikely to be caused
by any known disease does not make the link between the sonar and the harm
to the animals. Thus, (D) is the answer.
POE for Assumption Questions
When you’re using POE on Assumption questions, always eliminate
answer choices that do the following:
1. Give New Information. The assumption must link the
premise and the conclusion. Any answer choices that
discuss information that is not part of the original argument
are wrong.
2. Have the Wrong Tone. The tone of the answer choice
should match the tone of the argument. Arguments that
have very strong conclusions require very strongly worded
answer choices, and arguments that have milder tones
require milder answer choices.
3. Weaken the Argument. The assumption is necessary to
the argument. Eliminate any answer choice that would
weaken or hurt the argument—unless of course you’re
dealing with a Weaken question!
Strengthen Questions
Here’s another Critical Reasoning question:
Several companies have recently switched at least partially from memos written by
hand on printer paper to memos written on a computer and sent electronically with
no use of paper at all. Therefore, less printer paper will be used as a result of these
changes than would have been used if these companies had continued to use
handwritten memos.
Which of the following, if true, most strengthens the argument above?
Many of the companies that have switched to electronic memos have
increased the number of memos sent.
More printer paper was used to create manuals for the use of electronic
memos than was used to write handwritten memos.
Companies that used more printer paper were more likely to switch to
electronic memos than companies that used less printer paper.
Some of the industries that have switched at least partially to electronic
memos still primarily use printer paper for other operations.
The amount of printer paper needed to explain the electronic memos is less
than the amount that would have been used for handwritten memos.
Remember to identify the
question type first.
Here’s How to Crack It
Let’s again apply the four steps:
1. Read the Question Carefully. It’s a Strengthen question; we know
this because the word “strengthen” is actually used in the question!
2. Analyze the Argument. Find the premise, conclusion, and
assumption. Here’s what you should end up with:
Conclusion: Less printer paper will be used as a result of
electronic memos than would have been used with hand written
memos.
Why?
Premise: Several companies at least partially have switched from
handwritten memos on printer paper to memos written on a
computer and sent electronically.
Assumption: Companies use a lot of printer paper for handwritten
memos; companies will stop using printer paper for memos; the
amount of printer paper used for other operations won’t increase.
3. Know What the Answer Needs to Do. To strengthen an argument,
look for an answer that provides evidence that the assumption of
the argument is valid.
4. Use Process of Elimination. Check out the gray box on this page
for some POE guidelines on Strengthen questions.
Always check all five
answer choices.
Choice (A) introduces the concept that the number of memos has increased in
the companies that have switched to electronic memos. This does not
strengthen an argument that less paper is being used, so eliminate (A). Choice
(B) is a reversal of the passage, as this actually weakens the conclusion. If
more printer paper was used to produce manuals than would have been used
to write memos, then the amount of printer paper used overall would not
decrease. Eliminate (B).
Choice (C) mentions that companies that used more printer paper were more
likely to switch to electronic memos than those which used less printer paper.
However, this does not address whether the electronic memos caused less
printer paper to be used, as the companies using more printer paper prior to
switching may not have been using that paper to make handwritten memos.
Eliminate (C). Choice (D) indicates that companies that have switched to
electronic memos still use printer paper for other operations. This does not
strengthen the argument that less printer paper is being used, so eliminate (D).
Choice (E) indicates that less printer paper is used to initiate the change than
would have been used to write the memos, which would strengthen the claim
that the total amount of printer paper used would decrease. The correct
answer is (E).
POE for Strengthen Questions
When you’re using POE on Strengthen questions, always eliminate
answer choices that
1. Are Only Half Good. Some answers will be on the right
track, but they won’t strengthen the argument enough.
Again, remember that you’re looking for the correct
answer, not an answer that might be good enough. You
shouldn’t have to make any assumptions about the answer
choice in order for it to strengthen the argument.
2. Weaken the Argument. Typically, one of the answer
choices will weaken the argument. Unless your task is to
weaken the argument, you can easily eliminate it.
3. Do Nothing. Some answer choices do nothing to the
argument; they neither strengthen nor weaken it. Get rid of
these; they’re decoys.
On Strengthen questions, note that answer choices that offer new
information are okay, provided of course that they help strengthen the
argument. Also note that answers that have strong tones are often
correct for Strengthen questions.
Weaken Questions
Try one last Critical Reasoning question:
Psychologists have just completed an extensive study of recently divorced parents
in order to determine which factors contributed most to the dissolution of the
marriage. The researchers found that in a great majority of the cases of failed
marriages, the couples ate, on average, fewer than 10 meals per week with each
other. From this data, the psychologists have determined that a failure to spend
time together during meal times is a major factor leading to divorce.
Which of the following, if true, would cast the most doubt on the researchers’
hypothesis?
Many couples who have long and successful marriages eat together fewer
than ten times per week.
Most of the couples in the study who were unable to share meals with each
other worked outside of the home.
People who lack a regular dining schedule tend to have more disorders and
illnesses of the digestive system.
Couples in the study who reported that they ate together more than ten times
per week also indicated that they tended to perceive their relationships with
their spouses as healthy.
In many cases, people in unhappy marriages tend to express their
displeasure by avoiding contact with their partners when possible.
Do you recognize what
type of argument this is?
Here’s How to Crack It
This is a Weaken question. Once again, we’ll break the argument down into
its premise, conclusion, and assumption:
Conclusion: A failure to spend time together during meal times is a major
factor leading to divorce.
Why?
Premise: In a great majority of the cases of failed marriages, the couples ate,
on average, fewer than 10 meals per week with each other.
Assumption: A lack of time spent eating meals together causes marital
problems; there is no other cause.
The assumptions are, first, that there is no other cause, and second, that the
cause and effect are not reversed. Since we want to weaken this argument, we
want to find an answer that attacks one of these assumptions.
Check out the gray box for POE guidelines on Weaken questions.
Looking through the answer choices, you can probably see right away that
(A) is not the correct answer. The argument is not about what successful
couples do; it is only concerned with divorced couples. Move on. Choice (B)
doesn’t really do anything to the argument; it’s unclear how this information
would affect the causal link assumed in the argument. The same goes for (C):
All this choice indicates is that there may be other problems linked to eating
—it doesn’t address the connection between dining and marriage success.
Choice (D) seems like it might strengthen the argument. These couples are
reporting a link between eating together more and perceiving their marriages
as healthy. Eliminate this choice. Choice (E) is the answer. This answer
choice shows that the researchers have reversed the cause and effect. It is not
that a failure to dine together causes marital strife; rather, couples that are
already unhappy express it by not eating together. This weakens the argument,
and (E) is correct.
POE for Weaken Questions
The guidelines for Weaken questions are basically the same as those
for Strengthen questions. Eliminate any answer choices that
1. Are Half Good. Make sure the answer attacks the
assumption thoroughly.
2. Strengthen the Argument. Once again, one answer
usually does the opposite of the question task—eliminate
the odd man out.
3. Do Nothing. Some answer choices neither strengthen nor
weaken the argument: Eliminate them.
As is the case with Strengthen questions, new information and
extreme tones in Weaken questions need not be eliminated.
OTHER CRITICAL REASONING QUESTION
TYPES
The GRE also contains Inference and Resolve/Explain questions, which
require you to use different approaches from those you use for Weaken and
Strengthen questions. Let’s go through how to crack Inference and
Resolve/Explain questions now.
Inference and Resolve/Explain questions do not require you to find the
premise and conclusion.
Inference Questions
An inference is a conclusion that’s based on a set of given facts. You can
identify Inference questions because they’ll look a lot like the following:
If the statements above are true, which of the following must also be true?
Which of the following statements can be properly inferred from the information
above?
Based on the information above, which of the following can logically be
concluded?
Here’s an example:
The Mayville Fire Department always fills its employment vacancies “in-house”—
when a firefighter retires or leaves the force, his or her position is filled by
interviewing all qualified members of the Mayville Department who are interested
in the position. Only if this process fails to produce a qualified candidate does the
department begin interviewing potential employees from outside the department.
This year, the Mayville Fire Department has hired three new firefighters from
outside the department.
On Inference questions,
you don’t have to find the
premise and conclusion.
If the statements above are true, which of the following must also be true?
For the coming year, the Mayville Fire Department will be understaffed
unless it hires three additional firefighters.
Firefighters hired from outside the Mayville Fire Department take longer to
properly train for the job.
At the time of the vacancies in the Mayville Fire Department, either there
were no qualified in-house candidates or no qualified in-house candidates
were interested in the open positions.
The three firefighters who left the department had jobs for which no other
members of the Mayville Fire Department were qualified to fill.
The three new firefighters are the first new employees hired by the Mayville
Fire Department.
Here’s How to Crack It
Inference questions are often associated with Critical Reasoning passages that
are not structured like the clear-cut arguments we’ve seen thus far. Often
these wacky arguments don’t even have conclusions and premises; instead,
they might simply resemble a set of facts.
Our strategy for approaching these types of questions, of course, begins with
identifying them as Inference questions. However, for Step 2, don’t attempt to
identify a conclusion or premise; simply read the argument. If the argument is
complex or hard to follow, don’t spend too much time trying to untangle it.
Most of the work on Inference questions should be done when you get to the
answer choices.
For Inference questions, Step 3 is simple. You’re just looking for an answer
that is true based on the facts provided in the argument.
Check out the POE guidelines for Inference questions in the gray box on the
next page.
Can you prove your answer
choice? If not, eliminate it.
Let’s start with (A). This choice says that the department will be
“understaffed.” Is there any part of the argument that indicates that this is
true? Nope, so eliminate this choice. Choice (B) states that firefighters from
outside the department take longer to train, but the argument says nothing at
all about training. Eliminate this choice. Choice (C) states that either there
were no qualified candidates in house or there were no qualified candidates
interested in the jobs. Returning to the argument, we see that the hiring policy
is that a vacant “position is filled by interviewing all qualified members of the
Mayville Department who are interested in the position.” If this process fails,
the department goes outside the department for candidates. Thus, since
Mayville hired three new fire fighters from outside the department, (C) must
be true.
Let’s go through the remaining answers. Choice (D) is tempting, but on
inference questions, we need to make sure that every part of the answer
choice holds up to scrutiny. This answer states that no other members of the
department were qualified to take the open positions. This could be true;
however, based on the facts presented, it could also be true that there were
qualified members who simply weren’t interested in applying for the position.
Thus, (D) isn’t the best choice—it isn’t better than (C). Finally, (E) goes
beyond the information presented. There is no way of knowing whether these
new firefighters were the first new employees. Choice (C) is still the best.
POE for Inference Questions
On Inference questions, eliminate answer choices that
1. Go Beyond the Information. Stick to the facts on
inference questions. Avoid answers that are overly broad or
general.
2. Could Be True. The correct answer on an inference must be
true. Answers that might be true or could be true are no
good.
3. Use Extreme Language. Be suspicious of strong language.
The presence of words such as all, none, always, never, or
impossible often means that an answer choice is wrong.
The key to Inference questions is using Process of Elimination: Take
each answer choice and return to the argument to see if you can prove
that it’s true. If you can’t point to the part of the argument that
supports the answer choice, the answer is wrong.
Resolve/Explain
Some Critical Reasoning questions will present you with a paradox—a set of
facts that seem to contradict each other. On these questions, your task is to
find the answer choice that best explains the contradiction. You can recognize
these questions because they often contain the following phrases:
Which of the following choices would best explain the situation presented above?
Which of the following, if true, would best resolve the discrepancy above?
Which of the following, if true, best reconciles the seeming paradox above?
Take a look at the following example:
Over the past ten years, the emergence of digital file sharing technology has
threatened the traditional market for entire music albums. Internet users are now
able to download single songs from their favorite artists, enabling them to acquire
the songs they desire without having to purchase the entire album. Some music
industry leaders contend that this practice causes untold financial losses, as the cost
of individual songs is not enough to offset the money lost producing the songs that
were not purchased from the rest of the album. However, consumer groups report
that there has been an increase in the sales of entire music albums.
Which of the following, if true, would best explain the situation above?
Some consumers who have illegally downloaded songs from the Internet
have been sued by major record companies.
Research indicates that persons who engage in file-sharing or songdownloading are usually only casual music fans.
The music industry is developing new technology to help prevent users
from illegally downloading songs.
Music artists tend to release more material, on average, today than they did
10 years ago.
Entire music albums released now often include bonus features that are
appealing to fans, such as interviews with the band and music videos, that
are not available unless the entire album is purchased.
Here’s How to Crack It
Like Inference questions, Resolve/Explain questions require a slightly
different approach. Step 1 remains the same—read the question and identify
the question type. Once you’ve identified the question as a resolve/explain
question, read the critical-reasoning passage. However, instead of looking for
a premise and conclusion, for Step 2 you’re going to look for two facts that
are in conflict. The basic pattern for a resolve/explain argument is as follows:
Fact I:
But
Fact II:
For the argument in the example, two facts are in conflict:
Fact I: Internet users are able to download individual songs instead of
purchasing entire music albums.
But
Fact II: There has been an increase in entire music album sales.
For Resolve/Explain questions, the correct answer shows how both facts can
be true at the same time. Proceed to Step 4, use POE, and as you read each
answer choice, ask yourself the following question:
How can both Fact I and Fact II be true?
Check out the POE guidelines for Resolve/Explain questions in the gray box.
Let’s use Process of Elimination on the answer choices in our example. The
first answer choice doesn’t resolve the conflict. It might explain why fewer
users illegally download music, but it doesn’t explain why entire music album
sales have increased. Eliminate (A). Choice (B) does nothing to the paradox.
The fact that the people who download music are casual fans doesn’t really
explain anything. Like (A), (C) is partly correct; however, it doesn’t explain
the increase in sales. Also, the answer choice states that the industry is
“developing” technology; it doesn’t state that the technology has been
implemented yet. So this couldn’t affect the current situation. Choice (D)
doesn’t help much either. You might assume that more material on the market
means that sales could increase even with downloading, but that line of
thought requires you to fill in too many missing pieces. The correct answer
should do all the work. Look at (E). This choice states that entire music
albums feature bonus material that is not available unless the entire album is
purchased. This could explain both the fact that people are downloading
individual songs and that entire music album sales are increasing. Since (E) is
a more complete explanation, it’s the correct answer.
POE for Resolve/Explain Questions
On Resolve/Explain questions, you should eliminate answer choices
that
1. Do Nothing. Many wrong answers simply do nothing to the
paradox.
2. Are Only Half Right. Some answers will deal with only
half of the conflict. Make sure the answer you select
addresses both facts.
3. Worsen the Situation. Eliminate choices that appear to
make the situation worse.
WON’T ALL THIS TAKE TOO MUCH TIME?
While it may seem at first like you will need a lot of time to break down the
arguments and apply the strategies, you’ll get faster at doing this with
practice. It’s better to take your time and truly understand how the questions
work than to rush through the problems, only to get them wrong.
Working more slowly
increases your accuracy,
which increases your
GRE score!
Critical Reasoning Practice Set
In this practice set, follow the steps exactly as we have presented them.
Answers can be found in Part V.
1 of 5
In 1989, corporate tax rates in some regions of the United States fell to their lowest level in 15 years,
while the rates in other regions reached new highs. In 1974, similar conditions led to a large flight of
companies from regions with unfavorable corporate tax policies to regions with favorable policies.
There was, however, considerably less corporate flight in 1989.
Which of the following, if true about 1989, most plausibly accounts for the finding that there was less
corporate flight in 1989 ?
The regions with the most favorable corporate tax policies had many of the same types of
corporations as did those with unfavorable tax policies, but this was not true in 1974.
In contrast to 1974, office rental costs in the regions with the most favorable corporate tax
policies were significantly higher than rental costs in other areas of the country.
In contrast to 1974, in 1989, the areas with the most favorable corporate tax policies reaped the
most benefit from tax incentives, although the tax codes were particularly difficult to decipher.
Tax incentives offered by foreign countries were higher in 1989 than in 1974.
Individual tax incentives in the areas with favorable corporate tax policies were slightly lower
than they were 15 years earlier in areas with favorable corporate tax policies.
2 of 5
Aramayo: Our federal government seems to function most efficiently when decision-making
responsibilities are handled by only a few individuals. Therefore, our government should consolidate its
leadership and move away from a decentralized representative democracy.
Tello: But moving our government in this direction could violate our constitutional mission to provide
government of, for, and by the people.
Which of the following statements describes Tello’s response to Aramayo?
Tello contradicts the reasoning used by Aramayo.
Tello uncovers an assumption used in Aramayo’s reasoning.
Tello brings up a possible negative consequence of accepting Aramayo’s argument.
Tello reveals the circular reasoning used by Aramayo.
Tello shows that Aramayo overgeneralizes a very special situation.
3 of 5
Business computer systems are designed to make workers more productive by automating a portion of
the work that must be completed in a business process. As a result, the employee is free to perform
more tasks that require human attention. Although productivity may be lost during a learning period,
many businesses experience dramatic gains in productivity after installing a new computer system.
While discussing the connection between productivity gains and computer systems, a well-respected
business journal recently stated that the person who serves as the Chief Information Officer is the
consummate business computer system.
By comparing a Chief Information Officer to business computer systems, the journal implicitly argues
that
Chief Information Officers should always communicate the value of computer systems to their
companies
the productivity of a company can be increased through the hiring of a Chief Information Officer
many companies have not improved their productivity with new computer systems
Chief Information Officers are more effective than are new computer systems
the impact of a Chief Information Officer on a company’s productivity is difficult to measure
4 of 5
Whenever Joe does his laundry at the Main Street Laundromat, the loads turn out cleaner than they do
when he does his laundry at the Elm Street Laundromat. Laundry done at the Main Street Laundromat is
cleaner because the machines at the Main Street Laundromat use more water per load than do those at
the Elm Street Laundromat.
Which of the following statements, if true, helps support the conclusion above?
The clothes washed at the Elm Street Laundromat were, overall, less clean than those washed at
the Main Street Laundromat.
Joe uses the same detergent at both laundromats.
The machines at the Oak Street Laundromat use twice as much water as do those at the Main
Street Laundromat.
Joe does three times as much laundry at the Main Street Laundromat as he does at the Elm Street
Laundromat.
Joe tends to do his dirtier laundry at the Elm Street Laundromat.
5 of 5
According to the United States Postal Service bureau of information, the rate of complaints concerning
late delivery was 30 times higher in 1991 than in 1964. Because the United States Postal Service
changed neighborhood routes from a multiple-truck delivery system to a single-truck delivery system
between 1964 and 1991, the enormous increase in complaints must be a result of this systematic change.
Which of the following, if true, weakens the conclusion drawn above?
In 1991, most late-mail complaints were reported to the appropriate United States Postal Service
office, whereas in 1964 most were not.
Even in a multiple-truck delivery system, certain letters will arrive late.
According to the United States Postal Service bureau of information, most of the complaints
concerning late delivery in 1991 were about registered mail.
The bulk amount of mail processed by the United States Postal Service was not much larger in
1991 than it was in 1964, before the systemic change occurred.
The change in neighborhood routes from a multiple-truck to a single-truck delivery system
sometimes causes enormous increase in the price of stamps.
Summary
Most Critical Reasoning questions require you to break down an
argument. The conclusion is the main point of an argument. The
premise is the fact cited in support of the conclusion.
The assumption is used to link the premise and the conclusion with
each other. Without an assumption, an argument breaks down.
To crack a Critical Reasoning question, read the question first so you
understand the task. Some questions require you to identify the
conclusion and the premise of an argument. Others ask you to find the
assumption or to strengthen or weaken the argument.
After reading the question, break down the argument into its premise
and conclusion and, if necessary, the assumption.
Try to predict in your own words what the correct answer needs to do in
order to answer the question.
Chapter 8
Vocabulary for the GRE
Words, words, words. That’s what you’ll find in this chapter. The following
pages contain the Key Terms List, a list of some of the most common words
that appear on the GRE. There are also some handy tips on studying and
learning new vocabulary words and exercises to test your progress. Be
advised, though, that the words in the chapter ahead are just a starting point.
As you prepare for your GRE, keep your eyes open for words you don’t know
and look them up!
VOCAB, VOCAB, VOCAB
As much as ETS would like to claim that the GRE doesn’t rely much on
vocabulary, the simple fact remains that many of the questions, answer
choices, and reading passages contain some difficult vocabulary. You can’t
improve your score substantially without increasing your vocabulary. You
might think that studying vocabulary is the most boring part of preparing for
the GRE, but it’s one of the most important, and it’s also the one part of GRE
preparation that’s actually useful to you beyond the confines of the test itself.
And the more words that you recognize (and know the meaning of) on the
test, the easier it will be. So there’s no avoiding the importance of vocabulary
to your success on the GRE. Unfortunately, it is virtually impossible to fairly
test someone’s vocabulary on a standardized test. If you memorize 1,000
words and on test day none of those words appear, does that mean you have a
bad vocabulary? Of course not—it just means that you’ve been victimized by
the limitations of standardized testing.
This doesn’t mean that you should take a defeatist attitude toward learning
vocabulary! Even if you have only a few weeks before your test, you can still
expand your vocabulary and increase your prospects of doing better on the
GRE. One thing you have working in your favor is the fact that ETS loves to
do the same things over and over. The words we’ve collected for you in this
chapter are the words that appear most frequently on the GRE. So let’s get
started learning some new words!
Improving your vocabulary
is one of the most
important things you
can do to improve your
Verbal score.
LEARN TO LOVE THE DICTIONARY
Get used to looking up words. ETS uses words that it believes the average
college-educated adult should know. These words show up in newspaper and
magazine articles, in books, and in textbooks. If you see a word you don’t
know while studying for the GRE or elsewhere, it’s probably a good GRE
word. Look it up and make a flash card. Dictionaries will give you the
pronunciation, while digital apps can provide quick, handy look-ups for new
words. Looking up words is a habit. You may have to force yourself to do it in
the beginning, but it becomes more natural over time. Many of the techniques
in this book will help you on the GRE but don’t have much relevance in dayto-day life, but a great vocabulary and good vocabulary habits will add a
tremendous amount of value to your graduate school career and beyond.
Flashcards From Us
You can make your own
flashcards or you can buy
Essential GRE Vocabulary
flashcards from us!
Learning New Words
How will you remember all the new words you should learn for the test? By
developing a routine for learning new words. Here are some tips.
•
To learn words that you find on your own, get into the habit of
reading good books, magazines, and newspapers. Start paying
attention to words you come across for which you don’t know the
definition. You might be tempted to just skip these, as usual, but
train yourself to write them down and look them up.
•
When you look up the word, say it out loud, being careful to
pronounce it correctly. This will help you remember it.
•
When you look up a word in the dictionary, don’t assume that the
first definition is the only one you need to know. The first
definition may be an archaic one, or one that applies only in a
particular context, so scan through all the definitions.
•
Now that you’ve learned the dictionary’s definition of a new word,
restate it in your own words. You’ll find it much easier to
remember a word’s meaning if you make it your own.
•
Mnemonics—Use your imagination to create a mental image to fix
the new word in your mind. For example, if you’re trying to
remember the word voracious, which means having an insatiable
appetite for an activity or pursuit, picture an incredibly hungry
boar, eating huge piles of food. The voracious boar will help you
to recall the meaning of the word. The crazier the image, the
better.
•
Keep a vocabulary notebook, or make a file with a list of new
vocabulary words and put it on your desktop. Simply having a
notebook with you will remind you to be on the lookout for new
words, and using it will help you to remember the ones you
encounter. Writing something down also makes it easier to
memorize. Jot down the word when you find it, note its
pronunciation and definition (in your own words) when you look it
up, and jot down your mnemonic or mental image. You might also
copy the sentence in which you originally found the word, to
remind yourself of how the word looks in context.
•
Do the same thing with flash cards. Write the word on one side
and the pronunciation, the meaning, and perhaps a mental image
on the other. Stick five or six of your flash cards in your pocket
every morning and use them whenever you can. Stuck on a
delayed subway train? Look at your flashcards. Standing in a long
line at the bank? Look at your flashcards. Sick of engaging in
small talk with boring acquaintances? Look at your flashcards.
(Only kidding about that last one.)
•
Use your new word every chance you get. Make it part of your
life. Insert it into your speech at every opportunity. Developing a
powerful vocabulary requires lots of exercise.
•
Learn word roots. Many words share similar origins. By learning
these common roots, you’ll be better able to work with words
you’ve never seen before. A good dictionary should list the origin
and roots of the words in it.
Learn new words little by
little; don’t try to learn a
ton at once!
THE KEY TERMS LIST
You should start your vocabulary work by studying the Key Terms List, a list
we’ve compiled of some of the most frequently tested words on the GRE. We
put together this list by analyzing released GREs and keeping tabs on the test
to make sure that these words are still popular with ETS. At the very least,
answer choices that contain Key Terms make very good guesses on questions
for which you don’t know the answer. Each word on the Key Terms List is
followed by the part of speech and a brief definition for the word. Some of the
words on this list may have other definitions as well, but the definitions we
have given are the ones most likely to appear on the GRE.
We’ve broken the Key Terms List down into four groups of about 75 words
each. Don’t try to learn all four groups of words at once—work with one list
at a time. Write the words and their definitions down in a notebook or on flash
cards. It is very important to write them down yourself, because this will help
you remember them. Just glancing through the lists printed in this book won’t
be nearly as effective. Before doing the exercises for each group, spend some
time studying and learning the words first. Then use the exercises as a way to
test yourself. Answers for the matching exercises appear in Part V of this
book.
Key Terms Group 1
abscond (verb)
to depart clandestinely; to steal off and hide
aberrant (adj.)
deviating from the norm (noun form: aberration)
alacrity (noun)
eager and enthusiastic willingness
anomaly (noun)
deviation from the normal order, form, or rule;
abnormality (adj. form: anomalous)
approbation (noun)
an expression of approval or praise
arduous (adj.)
strenuous, taxing; requiring significant effort
assuage (verb)
to ease or lessen; to appease or pacify
audacious (adj.)
daring and fearless; recklessly bold (noun form:
audacity)
austere (adj.)
without adornment; bare; severely simple; ascetic
(noun form: austerity)
axiomatic (adj.)
taken as a given; possessing self-evident truth
(noun form: axiom)
canonical (adj.)
following or in agreement with accepted,
traditional standards (noun form: canon)
capricious (adj.)
inclined to change one’s mind impulsively; erratic,
unpredictable
censure (verb)
to criticize severely; to officially rebuke
chicanery (noun)
trickery or subterfuge
connoisseur (noun)
an informed and astute judge in matters of taste;
expert
convoluted (adj.)
complex or complicated
disabuse (verb)
to undeceive; to set right
discordant (adj.)
conflicting; dissonant or harsh in sound
disparate (adj.)
fundamentally distinct or dissimilar
effrontery (noun)
extreme boldness; presumptuousness
eloquent (adj.)
well-spoken, expressive, articulate (noun form:
eloquence)
enervate (verb)
to weaken; to reduce in vitality
ennui (noun)
dissatisfaction and restlessness resulting from
boredom or apathy
equivocate (verb)
to use ambiguous language with a deceptive intent
(adj. form: equivocal)
erudite (adj.)
very learned; scholarly (noun form: erudition)
exculpate (verb)
exonerate; to clear of blame
exigent (adj.)
urgent, pressing; requiring immediate action or
attention
extemporaneous (adj.)
improvised; done without preparation
filibuster (noun)
intentional obstruction, esp. using prolonged
speechmaking to delay legislative action
fulminate (verb)
to loudly attack or denounce
ingenuous (adj.)
artless; frank and candid; lacking in sophistication
inured (adj.)
accustomed to accepting something undesirable
irascible (adj.)
easily angered; prone to temperamental outbursts
laud (verb)
to praise highly (adj. form: laudatory)
lucid (adj.)
clear; easily understood
magnanimity (noun)
the quality of being generously noble in mind and
heart, esp. in forgiving (adj. form: magnanimous)
martial (adj.)
associated with war and the armed forces
mundane (adj.)
of the world; typical of or concerned with the
ordinary
nascent (adj.)
coming into being; in early developmental stages
nebulous (adj.)
vague; cloudy; lacking clearly defined form
neologism (noun)
a new word, expression, or usage; the creation or
use of new words or senses
noxious (adj.)
harmful, injurious
obtuse (adj.)
lacking sharpness of intellect; not clear or precise
in thought or expression
obviate (verb)
to anticipate and make unnecessary
onerous (adj.)
troubling; burdensome
paean (noun)
a song or hymn of praise and thanksgiving
parody (noun)
a humorous imitation intended for ridicule or
comic effect, esp. in literature and art
perennial (adj.)
recurrent through the year or many years;
happening repeatedly
perfidy (noun)
intentional breach of faith; treachery (adj. form:
perfidious)
perfunctory (adj.)
cursory; done without care or interest
perspicacious (adj.)
acutely perceptive; having keen discernment
(noun form: perspicacity)
prattle (verb)
to babble meaninglessly; to talk in an empty and
idle manner
precipitate (adj.)
acting with excessive haste or impulse
precipitate (verb)
to cause or happen before anticipated or required
predilection (noun)
a disposition in favor of something; preference
prescience (noun)
foreknowledge of events; knowing of events prior
to their occurring (adj. form: prescient)
prevaricate (verb)
to deliberately avoid the truth; to mislead
qualms (noun)
misgivings; reservations; causes for hesitancy
recant (verb)
to retract, esp. a previously held belief
refute (verb)
to disprove; to successfully argue against
relegate (verb)
to forcibly assign, esp. to a lower place or position
reticent (adj.)
quiet; reserved; reluctant to express thoughts and
feelings
solicitous (adj.)
concerned and attentive; eager
sordid (adj.)
characterized by filth, grime, or squalor; foul
sporadic (adj.)
occurring only occasionally, or in scattered
instances
squander (verb)
to waste by spending or using irresponsibly
static (adj.)
not moving, active, or in motion; at rest
stupefy (verb)
to stun, baffle, or amaze
stymie (verb)
to block; to thwart
synthesis (noun)
the combination of parts to make a whole (verb
form: synthesize)
torque (noun)
a force that causes rotation
tortuous (adj.)
winding, twisting; excessively complicated
truculent (adj.)
fierce and cruel; eager to fight
veracity (noun)
truthfulness, honesty
virulent (adj.)
extremely harmful or poisonous; bitterly hostile or
antagonistic
voracious (adj.)
having an insatiable appetite for an activity or
pursuit; ravenous
waver (verb)
to move to and fro; to sway; to be unsettled in
opinion
Group 1 Exercises
Match the following words to their definitions. Answers can be found in Part
V.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
improvised; without preparation
a newly coined word or expression
a song of joy and praise
to praise highly
truthfulness; honesty
artless; frank and candid
associated with war and the military
to retract a belief or statement
cursory; done without care or interest
troubling; burdensome
to criticize; to officially rebuke
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
veracity
recant
extemporaneous
stymie
paean
lucid
laud
onerous
tortuous
neologism
martial
12. winding; twisting; complicated
13. to block; to thwart
14. clear; easily understood
L. ingenuous
M. censure
N. perfunctory
Hold Up and Break
Did you just tackle Hit
Parade Group 1? Before
you jump into Group 2,
give yourself a break. Take
a walk, get some air, eat
a snack. Let the Group 1
words sink in before you
dive into Group 2.
Key Terms Group 2
abate (verb)
to lessen in intensity or degree
accolade (noun)
an expression of praise
adulation (noun)
excessive praise; intense adoration
aesthetic (adj.)
dealing with, appreciative of, or responsive to art
or the beautiful
ameliorate (verb)
to make better or more tolerable
ascetic (noun)
one who practices rigid self-denial, esp. as an act
of religious devotion
avarice (noun)
greed, esp. for wealth (adj. form: avaricious)
axiom (noun)
a universally recognized principle (adj. form:
axiomatic)
burgeon (verb)
to grow rapidly or flourish
bucolic (adj.)
rustic and pastoral; characteristic of rural areas
and their inhabitants
cacophony (noun)
harsh, jarring, discordant sound; dissonance (adj.
form: cacophonous)
canon (noun)
an established set of principles or code of laws,
often religious in nature (adj. form: canonical)
castigation (noun)
severe criticism or punishment (verb form:
castigate)
catalyst (noun)
a substance that accelerates the rate of a chemical
reaction without itself changing; a person or thing
that causes change
caustic (adj.)
burning or stinging; causing corrosion
chary (adj.)
wary; cautious; sparing
cogent (adj.)
appealing forcibly to the mind or reason;
convincing
complaisance (noun)
the willingness to comply with the wishes of
others (adj. form: complaisant)
contentious (adj.)
argumentative; quarrelsome; causing controversy
or disagreement
contrite (adj.)
regretful; penitent; seeking forgiveness (noun
form: contrition)
culpable (adj.)
deserving blame (noun form: culpability)
dearth (noun)
smallness of quantity or number; scarcity; a lack
demur (verb)
to question or oppose
didactic (adj.)
intended to teach or instruct
discretion (noun)
cautious reserve in speech; ability to make
responsible decisions (adj. form: discreet)
disinterested (adj.)
free of bias or self-interest; impartial
dogmatic (adj.)
expressing a rigid opinion based on unproved or
improvable principles (noun form: dogma)
ebullience (noun)
the quality of lively or enthusiastic expression of
thoughts and feelings (adj. form: ebullient)
eclectic (adj.)
composed of elements drawn from various sources
elegy (noun)
a mournful poem, esp. one lamenting the dead
(adj. form: elegiac)
emollient (adj.)/(noun)
soothing, esp. to the skin; making less harsh;
mollifying; an agent that softens or smoothes the
skin
empirical (adj.)
based on observation or experiment
enigmatic (adj.)
mysterious; obscure; difficult to understand (noun
form: enigma)
ephemeral (adj.)
brief; fleeting
esoteric (adj.)
intended for or understood by a small, specific
group
eulogy (noun)
a speech honoring the dead (verb form: eulogize)
exonerate (verb)
to remove blame
facetious (adj.)
playful; humorous
fallacy (noun)
an invalid or incorrect notion; a mistaken belief
(adj. form: fallacious)
furtive (adj.)
marked by stealth; covert; surreptitious
gregarious (adj.)
sociable; outgoing; enjoying the company of other
people
harangue (verb)/(noun)
to deliver a forceful or angry speech; ranting
speech or writing.
heretical (adj.)
violating accepted dogma or convention (noun
form: heresy)
hyperbole (noun)
an exaggerated statement, often used as a figure of
speech (adj. form: hyperbolic)
impecunious (adj.)
lacking funds; without money
incipient (adj.)
beginning to come into being or to become
apparent
inert (adj.)
unmoving; lethargic; sluggish
innocuous (adj.)
harmless; causing no damage
intransigent (adj.)
refusing to compromise (noun form:
intransigence)
inveigle (verb)
to obtain by deception or flattery
morose (adj.)
sad; sullen; melancholy
odious (adj.)
evoking intense aversion or dislike
opaque (adj.)
impenetrable by light; not reflecting light
oscillation (noun)
the act or state of swinging back and forth with a
steady, uninterrupted rhythm (verb form: oscillate)
penurious (adj.)
penny-pinching; excessively thrifty; ungenerous
pernicious (adj.)
extremely harmful in a way that is not easily seen
or noticed
peruse (verb)
to examine with great care (noun form: perusal)
pious (adj.)
extremely reverent or devout; showing strong
religious devotion (noun form: piety)
precursor (noun)
one that precedes and indicates or announces
another
preen (verb)
to dress up; to primp; to groom oneself with
elaborate care
prodigious (adj.)
abundant in size, force, or extent; extraordinary
prolific (adj.)
producing large volumes or amounts; productive
putrefy (verb)
to rot; to decay and give off a foul odor (adj. form:
putrid)
quaff (verb)
to drink deeply
quiescence (noun)
stillness; motionlessness; quality of being at rest
(adj. form: quiescent)
redoubtable (adj.)
awe-inspiring; worthy of honor
sanction (noun)/(verb)
authoritative permission or approval; a penalty
intended to enforce compliance; to give
permission or authority
satire (noun)
a literary work that ridicules or criticizes a human
vice through humor or derision (adj. form:
satirical)
squalid (adj.)
sordid; wretched and dirty as from neglect (noun
form: squalor)
stoic (adj.)
indifferent to or unaffected by pleasure or pain;
steadfast (noun form: stoicism)
supplant (verb)
to take the place of; to supersede
torpid (adj.)
lethargic; sluggish; dormant (noun form: torpor)
ubiquitous (adj.)
existing everywhere at the same time; constantly
encountered; widespread
urbane (adj.)
sophisticated; refined; elegant (noun form:
urbanity)
vilify (verb)
to defame; to characterize harshly
viscous (adj.)
thick; sticky (noun form: viscosity)
Group 2 Exercises
Match the following words to their definitions. Answers can be found in Part
V.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
brief; fleeting
a forceful or angry speech
arousing strong dislike or aversion
to free from blame or responsibility
arousing fear or awe; worthy of honor;
formidable
unexpectedly harmful
to drink deeply
stinging; corrosive; sarcastic; biting
impressively great in size, force, or
extent; enormous
greed; hunger for money
unmoving; lethargic
impartial; unbiased
lack; scarcity
to win over by deception, coaxing or
flattery
A.
B.
C.
D.
E.
pernicious
ephemeral
avarice
quaff
caustic
F.
G.
H.
I.
odious
dearth
inert
disinterested
J.
K.
L.
M.
N.
exonerate
inveigle
prodigious
harangue
redoubtable
Break Time!
How did you do in
Group 2? Take a moment
to relax and let your mind
rest before diving into
Group 3. Remember to do
this between each group
of words so you don’t
overload your brain!
Key Terms Group 3
acumen (noun)
keen, accurate judgment or insight
adulterate (verb)
to reduce purity by combining with inferior
ingredients
amalgamate (verb)
to combine several elements into a whole (noun
form: amalgamation)
archaic (adj.)
outdated; associated with an earlier, perhaps more
primitive, time
aver (verb)
to state as a fact; to declare or assert
bolster (verb)
to provide support or reinforcement
bombastic (adj.)
pompous; grandiloquent (noun form: bombast)
diatribe (noun)
a harsh denunciation
dissemble (verb)
to disguise or conceal; to mislead
eccentric (adj.)
departing from norms or conventions
endemic (adj.)
characteristic of or often found in a particular
locality, region, or people
evanescent (adj.)
tending to disappear like vapor; vanishing
exacerbate (verb)
to make worse or more severe
fervent (adj.)
greatly emotional or zealous (noun form: fervor)
fortuitous (adj.)
happening by accident or chance
germane (adj.)
relevant to the subject at hand; appropriate in
subject matter
grandiloquence (noun)
pompous speech or expression (adj. form:
grandiloquent)
hackneyed (adj.)
rendered trite or commonplace by frequent usage
halcyon (adj.)
calm and peaceful
hedonism (noun)
devotion to pleasurable pursuits, esp. to the
pleasures of the senses (a hedonist is someone
who pursues pleasure)
hegemony (noun)
the consistent dominance of one state or group
over others
iconoclast (noun)
one who attacks or undermines traditional
conventions or institutions
idolatrous (adj.)
given to intense or excessive devotion to
something (noun form: idolatry)
impassive (adj.)
revealing no emotion
imperturbable (adj.)
marked by extreme calm, impassivity, and
steadiness
implacable (adj.)
not capable of being appeased or significantly
changed
impunity (noun)
immunity from punishment or penalty
inchoate (adj.)
in an initial stage; not fully formed
infelicitous (adj.)
unfortunate; inappropriate
insipid (adj.)
lacking in qualities that interest, stimulate, or
challenge
loquacious (adj.)
extremely talkative (noun form: loquacity)
luminous (adj.)
characterized by brightness and the emission of
light
malevolent (adj.)
having or showing often vicious ill will, spite, or
hatred (noun form: malevolence)
malleable (adj.)
capable of being shaped or formed; tractable;
pliable
mendacity (noun)
the condition of being untruthful; dishonesty (adj.
form: mendacious)
meticulous (adj.)
characterized by extreme care and precision;
attentive to detail
misanthrope (noun)
one who hates all other humans (adj. form:
misanthropic)
mitigate (verb)
to make or become less severe or intense; to
moderate
obdurate (adj.)
unyielding; hardhearted; intractable
obsequious (adj.)
exhibiting a fawning attentiveness
occlude (verb)
to obstruct or block
opprobrium (noun)
disgrace; contempt; scorn
pedagogy (noun)
the profession or principles of teaching, or
instructing
pedantic (adj.)
overly concerned with the trivial details of
learning or education; show-offish about one’s
knowledge
penury (noun)
poverty; destitution
pervasive (adj.)
having the tendency to permeate or spread
throughout
pine (verb)
to yearn intensely; to languish; to lose vigor
pirate (verb)
to illegally use or reproduce
pith (noun)
the essential or central part
pithy (adj.)
precise and brief
placate (verb)
to appease; to calm by making concessions
platitude (noun)
a superficial remark, esp. one offered as
meaningful
plummet (verb)
to plunge or drop straight down
polemical (adj.)
controversial; argumentative
prodigal (adj.)
recklessly wasteful; extravagant; profuse; lavish
profuse (adj.)
given or coming forth abundantly; extravagant
proliferate (verb)
to grow or increase swiftly and abundantly
queries (noun)
questions; inquiries; doubts in the mind;
reservations
querulous (adj.)
prone to complaining or grumbling; peevish
rancorous (adj.)
characterized by bitter, long-lasting resentment
(noun form: rancor)
recalcitrant (adj.)
obstinately defiant of authority; difficult to
manage
repudiate (verb)
to refuse to have anything to do with; to disown
rescind (verb)
to invalidate; to repeal; to retract
reverent (adj.)
marked by, feeling, or expressing a feeling of
profound awe and respect (noun form: reverence)
rhetoric (noun)
the art or study of effective use of language for
communication and persuasion
salubrious (adj.)
promoting health or well-being
solvent (adj.)
able to meet financial obligations; able to dissolve
another substance
specious (adj.)
seeming true, but actually being fallacious;
misleadingly attractive; plausible but false
spurious (adj.)
lacking authenticity or validity; false; counterfeit
subpoena (noun)
a court order requiring appearance and/or
testimony
succinct (adj.)
brief; concise
superfluous (adj.)
exceeding what is sufficient or necessary
surfeit (verb)
an overabundant supply; excess; to feed or supply
to excess (noun form: a surfeit of supplies)
tenacity (noun)
the quality of adherence or persistence to
something valued; persistent determination (adj.
form: tenacious)
tenuous (adj.)
having little substance or strength; flimsy; weak
tirade (noun)
a long and extremely critical speech; a harsh
denunciation
transient (adj.)
fleeting; passing quickly; brief
zealous (adj.)
fervent; ardent; impassioned, devoted to a cause (a
zealot is a zealous person)
Group 3 Exercises
Match the following words to their definitions. Answers can be found in Part
V.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
brief; concise; tersely cogent
prone to complaining; whining
fawning; ingratiating
marked by bitter, deep-seated
resentment
controversial; argumentative
dominance of one state or group over
others
uninteresting; tasteless; flat; dull
thin; flimsy; of little substance
excess; overindulgence
wasteful; recklessly extravagant
to appease; to pacify with concessions
to assert; to declare; to allege; to state as
fact
pompous; grandiloquent
tending to vanish like vapor
A.
B.
C.
D.
hegemony
aver
insipid
pithy
E. placate
F. prodigal
G.
H.
I.
J.
K.
L.
querulous
surfeit
rancorous
bombastic
obsequious
evanescent
M. polemical
N. tenuous
What’s Your Strategy?
Do you find flashcards
helpful? Or do you prefer
word lists? Or smartphone
apps? Figure out the
strategy that works best
for you when it comes to
learning vocabulary and
stick to it!
Key Terms Group 4
acerbic (adj.)
having a sour or bitter taste or character; sharp;
biting
aggrandize (verb)
to increase in intensity, power, influence, or
prestige
alchemy (noun)
a medieval science aimed at the transmutation of
metals, esp. base metals into gold (an alchemist is
one who practices alchemy)
amenable (adj.)
agreeable; responsive to suggestion
anachronism (noun)
something or someone out of place in terms of
historical or chronological context
astringent (adj.)
having a tightening effect on living tissue; harsh;
severe; something with a tightening effect on
tissue
contiguous (adj.)
sharing a border; touching; adjacent
convention (noun)
a generally agreed-upon practice or attitude
credulous (adj.)
tending to believe too readily; gullible (noun form:
credulity)
cynicism (noun)
an attitude or quality of belief that all people are
motivated by selfishness (adj. form: cynical)
decorum (noun)
polite or appropriate conduct or behavior (adj.
form: decorous)
derision (noun)
scorn, ridicule, contemptuous treatment (adj.
form: derisive; verb form: deride)
desiccate (verb)
to dry out or dehydrate; to make dry or dull
dilettante (noun)
one with an amateurish or superficial interest in
the arts or a branch of knowledge
disparage (verb)
to slight or belittle
divulge (verb)
to disclose something secret
fawn (verb)
to flatter or praise excessively
flout (verb)
to show contempt for, as in a rule or convention
garrulous (adj.)
pointlessly talkative; talking too much
glib (adj.)
marked by ease or informality; nonchalant;
lacking in depth; superficial
hubris (noun)
overbearing presumption or pride; arrogance
imminent (adj.)
about to happen; impending
immutable (adj.)
not capable of change
impetuous (adj.)
hastily or rashly energetic; impulsive and
vehement
indifferent (adj.)
having no interest or concern; showing no bias or
prejudice
inimical (adj.)
damaging; harmful; injurious
intractable (adj.)
not easily managed or directed; stubborn;
obstinate
intrepid (adj.)
steadfast and courageous
laconic (adj.)
using few words; terse
maverick (noun)
an independent individual who does not go along
with a group or party
mercurial (adj.)
characterized by rapid and unpredictable change
in mood
mollify (verb)
to calm or soothe; to reduce in emotional intensity
neophyte (noun)
a recent convert; a beginner; novice
obfuscate (verb)
to deliberately obscure; to make confusing
obstinate (adj.)
stubborn; hard-headed; uncompromising
ostentatious (adj.)
characterized by or given to pretentious display;
showy
pervade (verb)
to permeate throughout (adj. form: pervasive)
phlegmatic (adj.)
calm; sluggish; unemotional
plethora (noun)
an overabundance; a surplus
pragmatic (adj.)
practical rather than idealistic
presumptuous (adj.)
overstepping due bounds (as of propriety or
courtesy); taking liberties
pristine (adj.)
pure; uncorrupted; clean
probity (noun)
adherence to highest principles; complete and
confirmed integrity; uprightness
proclivity (noun)
a natural predisposition or inclination
profligate (adj.)
excessively wasteful; recklessly extravagant (noun
form: profligacy)
propensity (noun)
a natural inclination or tendency; penchant
prosaic (adj.)
dull; lacking in spirit or imagination
pungent (adj.)
characterized by a strong, sharp smell or taste
quixotic (adj.)
foolishly impractical; marked by lofty romantic
ideals
quotidian (adj.)
occurring or recurring daily; commonplace
rarefy (verb)
to make or become thin, less dense; to refine
recondite (adj.)
hidden; concealed; difficult to understand; obscure
refulgent (adj.)
radiant; shiny; brilliant
renege (verb)
to fail to honor a commitment; to go back on a
promise
sedulous (adj.)
diligent; persistent; hard-working
shard (noun)
a piece of broken pottery or glass
soporific (adj.)
causing drowsiness; tending to induce sleep
sparse (adj.)
thin; not dense; arranged at widely spaced
intervals
spendthrift (noun)
one who spends money wastefully
subtle (adj.)
not obvious; elusive; difficult to discern
tacit (adj.)
implied; not explicitly stated
terse (adj.)
brief and concise in wording
tout (verb)
to publicly praise or promote
trenchant (adj.)
sharply perceptive; keen; penetrating
unfeigned (adj.)
genuine; not false or hypocritical
untenable (adj.)
indefensible; not viable; uninhabitable
vacillate (verb)
to waver indecisively between one course of
action or opinion and another
variegated (adj.)
multicolored; characterized by a variety of patches
of different color
vexation (noun)
annoyance; irritation (verb form: vex)
vigilant (adj.)
alertly watchful (noun form: vigilance)
vituperate (verb)
to use harsh condemnatory language; to abuse or
censure severely or abusively; to berate
volatile (adj.)
readily changing to a vapor; changeable; fickle;
explosive (noun form: volatility)
Group 4 Exercises
Match the following words to their definitions. Answers can be found in Part
V.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
acid or biting; bitter in taste or tone
sleep-inducing; causing drowsiness
a surplus; an overabundance
one with superficial interest in a subject
arrogance; overbearing pride
sharing a border; touching; adjacent
talking too much; rambling
something out of place in history or
chronology
difficult to understand; obscure; hidden
dull; unimaginative; ordinary
unemotional; calm
stubborn; obstinate; difficult to manage
or govern
13. condemn with harsh, abusive words;
berate
14. foolishly impractical; marked by lofty
A.
B.
C.
D.
E.
F.
G.
H.
anachronism
contiguous
dilettante
intractable
prosaic
quixotic
recondite
vituperate
I.
J.
K.
L.
acerbic
garrulous
hubris
soporific
M. phlegmatic
N. plethora
ideals
BEYOND THE KEY TERMS LIST
So you’ve finished the Key Terms List and you’re now the master of many
more words than you were before. What to do next? Why, go beyond the Key
Terms List of course! The Key Terms List was just the beginning. To
maximize your score on the GRE you must be relentless in increasing your
vocabulary. Don’t let up. Keep learning words until the day you sit down for
the exam. The following lists of extra words don’t have exercises, so just keep
working with your notebook or flash cards and get your friends to quiz you.
You are a vocabulary machine!
Beyond the Key Terms Group 1
The following list contains some of those simple-sounding words with less
common secondary meanings that ETS likes to test on the GRE.
alloy (verb)
to commingle; to debase by mixing with
something inferior; unalloyed means pure
appropriate (verb)
to take for one’s own use; to confiscate
arrest, arresting
(verb)/(adj.)
to suspend; to engage; holding one’s attention: as
in arrested adolescence, an arresting portrait
august (adj.)
majestic, venerable
bent (noun)
leaning, inclination, proclivity, tendency
broach (verb)
to bring up; to announce; to begin to talk about
brook (verb)
to tolerate; to endure; to countenance
cardinal (adj.)
major, as in cardinal sin
chauvinist (noun)
a blindly devoted patriot
color (verb)
to change as if by dyeing, i.e., to distort, gloss, or
affect (usually the first)
consequential (adj.)
pompous, self-important (primary definitions are:
logically following; important)
damp (verb)
to diminish the intensity or check the vibration of
a sound
die (noun)
a tool used for shaping, as in a tool-and-die shop
essay (verb)
to test or try; to attempt; to experiment
exact (verb)
to demand; to call for; to require; to take
fell (verb)
to cause to fall by striking
fell (adj.)
inhumanly cruel
flag (verb)
to sag or droop; to become spiritless; to decline
flip (adj.)
sarcastic, impertinent, as in flippant: a flip remark
ford (verb)
to wade across the shallow part of a river or
stream
grouse (verb)
to complain or grumble
guy (noun)
a rope, cord, or cable attached to something as a
brace or guide; to steady or reinforce using a guy:
Think guide. (verb form: guyed, guying)
intimate (verb)
to imply, suggest, or insinuate
list (verb)
to tilt or lean to one side
lumber (verb)
to move heavily and clumsily
meet (adj.)
fitting, proper
milk (verb)
to exploit; to squeeze every last ounce of
mince (verb)
to pronounce or speak affectedly; to euphemize, to
speak too carefully. Also, to take tiny steps; to
tiptoe
nice (adj.)
exacting, fastidious, extremely precise
occult (adj.)
hidden, concealed, beyond comprehension
pedestrian (adj.)
commonplace, trite, unremarkable, quotidian
pied (adj.)
multicolored, usually in blotches
pine (verb)
to lose vigor (as through grief); to yearn
plastic (adj.)
moldable, pliable, not rigid
pluck (noun)
courage, spunk, fortitude
prize (verb)
to pry, to press or force with a lever; something
taken by force, spoils
rail (verb)
to complain about bitterly
rent (verb)
torn (past tense of rend); an opening or tear caused
by such
quail (verb)
to lose courage; to turn frightened
qualify (verb)
to limit
sap (verb)
to enervate or weaken the vitality of
sap (noun)
a fool or nitwit
scurvy (adj.)
contemptible, despicable
singular (adj.)
exceptional, unusual, odd
stand (noun)
a group of trees
steep (verb)
to saturate or completely soak, as in to let a tea
bag steep
strut (noun)
the supporting structural cross-part of a wing
table (verb)
to remove (as a parliamentary motion) from
consideration
tender (verb)
to proffer or offer
waffle (verb)
to equivocate; to change one’s position
wag (noun)
wit, joker
Beyond the Key Terms Group 2
abjure (verb)
to renounce or reject solemnly; to recant; to avoid
adumbrate (verb)
to foreshadow vaguely or intimate; to suggest or
outline sketchily; to obscure or overshadow
anathema (noun)
a solemn or ecclesiastical (religious) curse;
accursed or thoroughly loathed person or thing
anodyne (adj.)/(noun)
soothing; something that assuages or allays pain
or comforts
apogee (noun)
farthest or highest point; culmination; zenith
apostate (noun)
one who abandons long-held religious or political
convictions
apotheosis (noun)
deification; glorification to godliness; an exalted
example; a model of excellence or perfection
asperity (noun)
severity, rigor; roughness, harshness; acrimony,
irritability
asseverate (verb)
to aver, allege, or assert
assiduous (adj.)
diligent, hard-working, sedulous
augury (noun)
omen, portent
bellicose (adj.)
belligerent, pugnacious, warlike
calumniate (verb)
to slander, to make a false accusation; calumny
means slander, aspersion
captious (adj.)
disposed to point out trivial faults; calculated to
confuse or entrap in argument
cavil (verb)
to find fault without good reason
celerity (noun)
speed, alacrity; think accelerate
chimera (noun)
an illusion; originally, an imaginary fire-breathing
she-monster
contumacious (adj.)
insubordinate, rebellious; contumely means insult,
scorn, aspersion
debacle (noun)
rout, fiasco, complete failure
denouement (noun)
an outcome or solution; the unraveling of a plot
descry (verb)
to catch sight of
desuetude (noun)
disuse
desultory (adj.)
random; aimless; marked by a lack of plan or
purpose
diaphanous (adj.)
transparent, gauzy
diffident (adj.)
reserved, shy, unassuming; lacking in selfconfidence
dirge (noun)
a song of grief or lamentation
encomium (noun)
glowing and enthusiastic praise; panegyric,
tribute, eulogy
eschew (verb)
to shun or avoid
excoriate (verb)
to censure scathingly, to upbraid
execrate (verb)
to denounce, to feel loathing for, to curse, to
declare to be evil
exegesis (noun)
critical examination, explication
expiate (verb)
to atone or make amends for
extirpate (verb)
to destroy, to exterminate, to cut out, to exscind
fatuous (adj.)
silly, inanely foolish
fractious (adj.)
quarrelsome, rebellious, unruly, refractory,
irritable
gainsay (verb)
to deny, to dispute, to contradict, to oppose
heterodox (adj.)
unorthodox, heretical, iconoclastic
imbroglio (noun)
difficult or embarrassing situation
indefatigable (adj.)
not easily exhaustible; tireless, dogged
ineluctable (adj.)
certain, inevitable
inimitable (adj.)
one of a kind, peerless
insouciant (adj.)
unconcerned, carefree, heedless
inveterate (adj.)
deep rooted, ingrained, habitual
jejune (adj.)
vapid, uninteresting, nugatory; childish, immature,
puerile
lubricious (adj.)
lewd, wanton, greasy, slippery
mendicant (noun)
a beggar, supplicant
meretricious (adj.)
cheap, gaudy, tawdry, flashy, showy; attracting by
false show
minatory (adj.)
menacing, threatening (reminds you of the
Minotaur, a threatening creature indeed)
nadir (noun)
low point, perigee
nonplussed (adj.)
baffled, bewildered, at a loss for what to do or
think
obstreperous (adj.)
noisily and stubbornly defiant, aggressively
boisterous
ossified (adj.)
tending to become more rigid, conventional,
sterile, and reactionary with age; literally, turned
into bone
palliate (verb)
to make something seem less serious, to gloss
over, to make less severe or intense
panegyric (noun)
formal praise, eulogy, encomium; panegyrical
means expressing elaborate praise
parsimonious (adj.)
cheap, miserly
pellucid (adj.)
transparent, easy to understand, limpid
peroration (noun)
the concluding part of a speech; flowery,
rhetorical speech
plangent (adj.)
pounding, thundering, resounding
prolix (adj.)
long-winded, verbose; prolixity means verbosity
propitiate (verb)
to appease; to conciliate; propitious means
auspicious, favorable
puerile (adj.)
childish, immature, jejune, nugatory
puissance (noun)
power, strength; puissant means powerful, strong
pusillanimous (adj.)
cowardly, craven
remonstrate (verb)
to protest, to object
sagacious (adj.)
having sound judgment; perceptive, wise; like a
sage
salacious (adj.)
lustful, lascivious, bawdy
salutary (adj.)
remedial, wholesome, causing improvement
sanguine (adj.)
cheerful, confident, optimistic
saturnine (adj.)
gloomy, dark, sullen, morose
sententious (adj.)
aphoristic or moralistic; epigrammatic; tending to
moralize excessively
stentorian (adj.)
extremely loud and powerful
stygian (adj.)
gloomy, dark
sycophant (noun)
toady, servile, self-seeking flatterer; parasite
tendentious (adj.)
biased; showing marked tendencies
timorous (adj.)
timid, fearful, diffident
tyro (noun)
novice, greenhorn, rank amateur
vitiate (verb)
to corrupt, to debase, to spoil, to make ineffective
voluble (adj.)
fluent, verbal, having easy use of spoken language
Part III
How to Crack the Math Section
9
The Geography of the Math Section
10 Math Fundamentals
11 Algebra (And When to Use It)
12 Real World Math
13 Geometry
14 Math Et Cetera
Chapter 9
The Geography of the Math Section
This chapter contains an overview of the content and structure you’ll see on
the Math section of the GRE. It provides valuable information on pacing
strategies and the various question formats you’ll encounter on the GRE. It
also goes over how to use basic test-taking techniques such as Process of
Elimination and Ballparking as they relate to math questions. After finishing
this chapter, you’ll have a good idea of what the Math section of the GRE
looks like and some basic approaches to help you navigate it.
WHAT’S IN THE MATH SECTION
The GRE Math section primarily tests math concepts you learned in seventh
through tenth grades, including arithmetic, algebra, and geometry. ETS
alleges that the Math section tests the reasoning skills that you’ll use in
graduate school, but what the Math section primarily tests is your comfort
level with some basic math topics and your ability to take a test with strangelooking questions under timed conditions.
The Math section of the exam consists of two 35-minute sections, each of
which will consist of 20 questions. The first 7 or 8 questions of each section
will be quantitative comparisons (quant comp, for short). The remainder will
consist of multiple-choice or numeric-entry questions.
Junior High School?
The Math section of the GRE mostly tests how much you remember
from the math courses you took in seventh, eighth, ninth, and tenth
grades. But here’s some good news: GRE math is easier than SAT
math. Why? Because many people study little or no math in college.
If the GRE tested college-level math, everyone but math majors
would bomb the test.
If you’re willing to do a little work, this is good news for you. By
brushing up on the modest amount of math you need to know for the
test, you can significantly increase your GRE Math score. All you
have to do is shake off the dust.
Predictable Questions
The beauty of a standardized test is that it is, well, standardized. Standardized
means predictable. We know exactly what ETS is going to test and how
they’re going to test it. The math side of the test consists of a series of utterly
predictable questions, to which we have designed a series of highly scripted
responses. ETS wants you to see each problem as a new challenge to solve.
What you will find, however, is that there are only about 20 math concepts
that are being tested. All of the questions you will see are just different ways
of asking about these different concepts. Most of these concepts you already
know. Once you recognize what’s being tested, even the trickiest questions
become familiar and easy to solve.
It’s Really a Reading Test
In constructing the Math section, ETS is limited to the math that nearly
everyone has studied: arithmetic, basic algebra, basic geometry, and
elementary statistics. There’s no calculus (or even precalculus), no
trigonometry, and no major-league algebra or geometry. Because of these
limitations, ETS has to resort to traps in order to create hard problems. Even
the most commonly missed GRE math problems are typically based on
relatively simple principles. What makes the problems difficult is that these
simple principles are disguised.
Many test takers have no problem doing the actual calculations involved in
the math questions on the GRE; in fact, you’ll even be allowed to use a
calculator (more on that soon). However, on this test your ability to carefully
read the problems and figure out how to set them up is more important than
your ability to make calculations.
Head to your Premium
Portal to watch topnotch Princeton Review
instructors talk about the
GRE Math section and
walk you through sample
problems.
As you work through this section, don’t worry about how quickly you’re
doing the problems. Instead, take the time to really understand what the
questions are asking; pay close attention to the wording of the problems. Most
math errors are the result of careless mistakes caused by not reading the
problem carefully enough!
Read and Copy Carefully
You can do all the calculations right and still get a question wrong. How?
What if you solve for x but the question asked for the value of x + 4? Ugh.
Always reread the question before you choose an answer. Take your time and
don’t be careless. The problem will stay on the screen as long as you want it
to, so reread the question and double-check your work before answering it.
Or how about this? The radius of the circle is 5, but when you copied the
picture onto your scratch paper, you accidentally made it 6. Ugh! If you make
a mistake copying down information from the screen, you’ll get the question
wrong no matter how perfect your calculations are. You have to be extra
careful when copying down information.
THE CALCULATOR
As we mentioned before, on the GRE you’ll be given an on-screen calculator.
The calculator program on the GRE is a rudimentary one that gives you the
five basic operations: addition, subtraction, multiplication, division, and
square root, plus a decimal function and a positive/negative feature. It follows
the order of operations, or PEMDAS (more on this topic in Chapter 10). The
calculator also has the ability to transfer the answer you’ve calculated directly
into the answer box for certain questions. The on-screen calculator can be a
huge advantage—if it’s used correctly!
As you might have realized by this point, ETS is not exactly looking out for
your best interests. Giving you a calculator might seem like an altruistic act,
but rest assured that ETS knows that there are certain ways in which
calculator use can be exploited. Keep in mind the following:
1. Calculators Can’t Think. Calculators are good for one thing and
one thing only: calculation. You still have to figure out how to set
up the problem correctly. If you’re not sure what to calculate, then
a calculator isn’t helpful. For example, if you do a percent
calculation on your calculator and then hit “Transfer Display,” you
will have to remember to move the decimal point accordingly,
depending on whether the question asks for a percent or a decimal.
2. The Calculator Can Be a Liability. ETS will give you questions
that you can solve with a calculator, but the calculator can actually
be a liability. You will be tempted to use it. For example, students
who are uncomfortable adding, subtracting, multiplying, or
dividing fractions may be tempted to convert all fractions to
decimals using the calculator. Don’t do it. You are better off
mastering fractions than avoiding them. Working with exponents
and square roots is another way in which the calculator will be
tempting but may yield really big and awkward numbers or long
decimals. You are much better off learning the rules of
manipulating exponents and square roots. Most of these problems
will be faster and cleaner to solve with rules than with a calculator.
The questions may also use numbers that are too big for the
calculator. Time spent trying to get an answer out of a calculator for
problems involving really big numbers will be time wasted. Find
another way around.
3. A Calculator Won’t Make You Faster. Having a calculator
should make you more accurate, but not necessarily faster. You still
need to take time to read each problem carefully and set it up.
Don’t expect to blast through problems just because you have a
calculator.
4. The Calculator Is No Excuse for Not Using Scratch Paper.
Scratch paper is where good technique happens. Working problems
by hand on scratch paper will help to avoid careless errors or
skipped steps. Just because you can do multiple functions in a row
on your calculator does not mean that you should be solving
problems on your calculator. Use the calculator to do simple
calculations that would otherwise take you time to solve. Make
sure you are still writing steps out on your scratch paper, labeling
results, and using set-ups. Accuracy is more important than speed!
Of course, you should not fear the calculator; by all means, use it and be
grateful for it. Having a calculator should help you eliminate all those careless
math mistakes.
GEOGRAPHY OF A MATH SECTION
Each of the two Math sections contains 20 questions. Test takers are allowed
35 minutes per section. The first 7 or 8 questions of each Math section are
quantitative comparisons, while the remainder are a mixed bag of problem
solving, all that apply, numeric entry, and charts and graphs. Each section
covers a mixture of algebra, arithmetic, quantitative reasoning, geometry, and
real-world math.
QUESTION FORMATS
Much like the Verbal section, the Math portion of the GRE contains a variety
of different question formats. Let’s go through each type of question and
discuss how to crack it.
Standard Multiple Choice
These questions are the basic five-answer multiple-choice questions. These
are great candidates for POE (Process of Elimination) strategies we will
discuss later in this chapter.
Multiple Choice, Multiple Answer
These questions appear similar to the standard multiple-choice questions;
however, on these you will have the opportunity to pick more than one
answer. There can be anywhere from three to eight answer choices. Here’s an
example of what these will look like:
If
< x < , then which of the following could be the value of x ?
Indicate all such values.
Your approach on these questions won’t be radically different from the
approach you use on standard multiple-choice questions. But obviously,
you’ll have to consider all of the answers—make sure you read each question
carefully and remember that more than one answer can be correct. For
example, for this question, you’d click on (C) and (D). You must select every
correct choice to get credit for the problem.
Quantitative Comparison Questions
Quantitative comparison questions, hereafter affectionately known as “quant
comp” questions, ask you to compare Quantity A to Quantity B. These
questions have four answer choices instead of five, and all quant comp answer
choices are the same. Here they are:
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Your job is to compare the two quantities and choose one of these answers.
Quant comp problems test the same basic arithmetic, algebra, and geometry
concepts as do the other GRE math problems. So, to solve these problems,
you’ll apply the same techniques you use on the other GRE math questions.
But quant comps also have a few special rules you need to remember.
There Is No “(E)”
Because there are only four choices on quant comp questions, after you use
POE to eliminate all of the answer choices you can, your odds of guessing
correctly are even better. Think about it this way: Eliminating even one
answer on a quant comp question will give you a one-in-three chance of
guessing correctly.
If a Quant Comp Question Contains Only Numbers, the
Answer Can’t Be (D)
Any quant comp problem that contains only numbers and no variables must
have a single solution. Therefore, on these problems, you can eliminate (D)
immediately because the larger quantity can be determined. For example, if
you’re asked to compare
and , you can determine which fraction is larger,
so the answer cannot be (D).
Compare, Don’t Calculate
You don’t always have to calculate the exact value of each quantity before
you compare them. After all, your mission is simply to compare the two
quantities. It’s often helpful to treat the two quantities as though they were
two sides of an equation. Anything you can do to both sides of an equation,
you can also do to both quantities. You can add the same number to both
sides, you can multiply both sides by the same positive number, and you can
simplify a single side by multiplying it by one.
Do only as much work
as you need to.
If you can simplify the terms of a quant comp, you should always do so.
Here’s a quick example:
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
Don’t do any calculating! Remember: Do only as much work as you need to
in order to answer the question! The first thing you should do is eliminate (D).
After all, there are only numbers here. After that, get rid of numbers that are
common to both columns (think of this as simplifying). Both columns contain
a
and a
, so because we’re talking about addition, they can’t make a
difference to the outcome. With them gone, you’re merely comparing the
column A to the
in
in column B. Now we can eliminate (C) as well—after all,
there is no way that
is equal to . So, we’re down to two choices, (A) and
(B). If you don’t remember how to compare fractions, don’t worry—it’s
covered in Chapter 10 (Math Fundamentals). The answer to this question is
(B).
Okay, let’s talk about another wacky question type you’ll see in the Math
section.
Numeric Entry
Some questions on the GRE won’t even have answer choices, and you’ll have
to generate your own answer. Here’s an example:
Each month, Renaldo earns a commission of 10.5% of his total sales for the month,
plus a salary of $2,500. If Renaldo earns $3,025 in a certain month, what were his
total sales?
Here’s How to Crack It
On this type of question, POE is not going to help you! That means if you’re
not sure how to do one of these questions, you should immediately move on.
Leave it blank and come back to it in your second pass through the test.
If Renaldo earned $3,025, then his earnings from the commission on his sales
are $3,025 − $2,500 = $525. So, $525 is 10.5% of his sales. Set up an
equation to find the total sales: 525 =
, where x is the amount of
the sales. Solving this equation, x = 5,000. (We’ll review how to set up and
solve equations like this in later chapters.)
To answer this question, you’d enter 5000 into the box. Alternately, you could
transfer your work directly from the on-screen calculator to the text box.
MAXIMIZE YOUR SCORE
As you’re probably aware by now, doing well on the Math section will
involve more than just knowing some math. It will also require the use of
some good strategies. Let’s go through some good strategies now. Make sure
you read this section carefully; it will be important for you to keep these
techniques in mind as you work through the content chapters that follow this
one!
The Two Roles of Techniques
The techniques are there to ensure that the questions that you should get
right, you do get right. A couple of careless errors on easy questions will kill
your score. The techniques are not just tools; they are proven standard
approaches that save time and effort and guarantee points. Use these
techniques on every question. Turn them into habits that you use every time.
Take the Easy Test First
The GRE offers the opportunity to mark a question and return to it. Since all
questions count equally toward your score, why not do the easy ones first?
Getting questions right is far more important than getting to every question,
so start with the low hanging fruit. There is no law that says you have to take
the test in the order in which it is given. If you see a question you don’t like,
keep moving. Play to your strengths and get all of the questions that you’re
good at in the bank, before you start spending time on the hard ones. It makes
no sense to spend valuable minutes wrestling with hard questions while there
are still easy ones on the table. It makes even less sense if you end up having
to rush some easy ones (making mistakes in the process), as a result. Free
yourself from numerical hegemony! Take the easy test first!
Bend, Don’t Push
Eighty percent of the errors on the math side of the test are really reading
errors. The GRE is nearly a four-hour-long test, so at some point during this
time your brain will get tired. When this happens you will read, see, or
understand questions incorrectly. Once you see a problem wrong, it is nearly
impossible to see it correctly. When this happens, even simple problems can
become extremely frustrating. If you solve a problem and your answer is not
one of the choices, this is what has happened. When you would swear that a
problem can’t be solved, this is what has happened. When you have
absolutely no idea how to solve a problem, this is what has happened. If you
find yourself with half a page full of calculations and are no closer to the
answer, this is what has happened. When you find yourself in this scenario,
you can continue to push on that problem all day and you won’t get any
closer.
There is a good chance that you are already familiar with this frustration. The
first step is to learn to recognize it when it is happening. Here are some keys
to recognizing when you are off track.
You know you are off track when…
•
You have spent more than three minutes on a single problem.
•
Your hand is not moving.
•
You don’t know what to do next.
•
Your answer is not one of the choices.
•
You’re spending lots of time with the calculator and working with
some ugly numbers.
Once you recognize that you are off track, stop and take a deep breath. Then
move on to the next question. Continuing to push on a problem, at this point,
is a waste of your time. You could easily spend three or four precious minutes
on this problem and be no closer to the answer. Spend those three or four
minutes on other questions. That time should be yielding you points, not
frustration.
After you have done two or three other questions, return to the one that was
giving you trouble. Most likely, the reason it was giving you trouble is that
you missed something or misread something the first time around. If the
problem is still difficult, walk away again.
This is called Bend, Don’t Push. The minute you encounter any resistance on
the test, walk away. Bend. There are plenty of other easier points for you to
get with that time. Then return to the problem a few questions later. It’s okay
to take two or three runs at a tough problem. If you run out of time before
returning to the question, so be it. Your time is better spent on easier problems
anyway, since all problems count the same.
Forcing yourself to walk away can be difficult, especially when you have
already invested time in a question. You will have to train yourself to
recognize resistance when it occurs, to walk away, and then to remember to
come back. Employ this technique anytime you are practicing for the GRE. It
will take some time to master. Be patient and give it a chance to work. With
this technique, there are no questions that are out of your reach on the GRE.
POE: Ballparking and Trap Answers
Use Process of Elimination whenever you can on questions that are in
standard multiple-choice format. Always read the answer choices before you
start to solve a math problem because often they will help guide you—you
might even be able to eliminate a couple of answer choices before you begin
to calculate the answer.
Two effective POE tools are Ballparking and Trap Answers.
You Know More Than You Think
Say you were asked to find 30 percent of 50. Wait—don’t do any math yet.
Let’s say that you glance at the answer choices and you see these:
5
15
30
80
150
Think about it. Whatever 30 percent of 50 is, it must be less than 50, right? So
any answer choice that’s greater than 50 can’t be right. That means you
should eliminate both (D) and (E) before you even do any calculations! Thirty
percent is less than half, so we can get rid of anything greater than 25, which
means that (C) is gone too. What is 10 percent of 50? Eliminate (A). You’re
done. The only answer left is (B). This process is known as Ballparking.
Remember that the answers are part of the question. There are more than four
times the number of wrong answers on the GRE as there are right ones. If it
were easy to find the right ones, you wouldn’t need this book. It is almost
always easier to identify and eliminate the wrong answers than it is to
calculate the right one. Just make sure that you are using your scratch paper to
eliminate answer choices instead of keeping track in your head.
Ballparking helps you eliminate answer choices and increases your odds of
zeroing in on the correct answer. The key is to eliminate any answer choice
that is “out of the ballpark.”
Need More Math
Review?
Check out Math Workout
for the GRE for even more
math practice.
Let’s look at another problem:
A 100-foot rope is cut so that the shorter piece is
the length of the longer piece.
What is the length of the shorter piece in feet?
75
66
50
40
33
Here’s How to Crack It
Now, before we dive into the calculations, let’s use a little common sense.
The rope is 100 feet long. If we cut the rope in half, each part would be 50
feet. However, we didn’t cut the rope in half; we cut it so that there’s a longer
part and a shorter part. What has to be true of the shorter piece then? It has to
be less than 50 feet. If it weren’t, it wouldn’t be shorter than the other piece.
So looking at our answers, we can eliminate (A), (B), and (C) without doing
any real math. That’s Ballparking. By the way, the answer is (D).
Trap Answers
ETS likes to include “trap answers” in the answer choices to their math
problems. Trap answers are answer choices that appear correct upon first
glance. Often these answers will look so tempting that you’ll choose them
without actually bothering to complete the necessary calculations. Watch out
for this! If a problem seems way too easy, be careful and double-check your
work.
Look at the this problem:
The price of a jacket is reduced by 10%. During a special sale, the price is
discounted by another 10%. The special sale price is what percent less than the
original price of the jacket?
15%
19%
20%
21%
25%
Here’s How to Crack It
The answer might seem like it should be 20 percent. But wait a minute: Does
it seem likely that the GRE is going to give you a problem that you can solve
just by adding 10 + 10? Probably not. Choice (C) is a trap answer.
To solve this problem, imagine that the original price of the jacket is $100.
After a 10 percent discount the new price is $90. But now when we take
another 10 percent discount, we’re taking it from $90, not $100. 10 percent of
90 is 9, so we take off another $9 from the price and our final price is $81.
That represents a 19 percent total discount because we started with a $100
jacket. The correct answer is (B).
HOW TO STUDY
Make sure you learn the content of each of the following chapters before you
go on to the next one. Don’t try to cram everything in all at once. It’s much
better to do a small amount of studying each day over a longer period; you
will master both the math concepts and the techniques if you focus on the
material a little bit at a time. Just as we have been telling you in earlier
chapters, let the content sink in by taking short study breaks between study
sessions and giving yourself plenty of time to prepare for the GRE. Slow and
steady wins the race!
Practice, Practice, Practice
Practice may not make perfect, but it sure will help. Use everyday math
calculations as practice opportunities. Balance your checkbook without a
calculator! Make sure your check has been added correctly at a restaurant, and
figure out the exact percentage you want to leave for a tip. The more you
practice simple adding, subtracting, multiplying, and dividing on a day-to-day
basis, the more your arithmetic skills will improve for the GRE.
After you work through this book, be sure to practice doing questions on our
online tests and on real GREs. There are always sample questions at
www.ets.org/gre, and practice will rapidly sharpen your test-taking skills.
Finally, unless you trust our techniques, you may be reluctant to use them
fully and automatically on the real GRE. The best way to develop that trust is
to practice before you get to the real test.
Your Premium Portal contains tons of informational
videos, practice tests,
helpful articles, and more
to help with your GRE
preparation. Head over
there and take advantage
of this fantastic resource!
Summary
The GRE contains two 35-minute Math sections. Each section has 20
questions.
The GRE tests math concepts up to about the tenth-grade level of
difficulty.
You will be allowed to use a calculator on the GRE. The calculator is
part of the on-screen display.
The Math section employs a number of different question formats,
including multiple choice, numeric entry, and quantitative comparison
questions.
Use the Two-Pass system on the Math section. Find the easier questions
and do them first. Use your remaining time to work some of the more
difficult questions.
When you get stuck on a problem, walk away. Do a few other problems
to distract your brain, and then return to the question that was giving
you problems.
Ballpark or estimate the answers to math questions and eliminate
answers that don’t make sense.
Watch out for trap answers. If an answer seems too easy or obvious, it’s
probably a trap.
Always do your work on your scratch paper, not in your head. Even
when you are Ballparking, make sure that you are eliminating answer
choices on your scratch paper. If your hand isn’t moving, you’re stuck
and you need to walk away, or you’re doing work in your head, which
leads to errors.
Chapter 10
Math Fundamentals
Numbers and equations form the basis of all the math questions on the GRE.
Simply put, the more comfortable you are working with numbers and
equations, the easier the math portion of the exam will be. This chapter gives
you a review of all the basic mathematical concepts including properties of
numbers, factors and multiples, fractions and decimals, math vocabulary, and
some basic rules of math.
GET FAMILIAR
To do well on the GRE Math section, you’ll have to be comfortable working
with numbers. The concepts tested on the GRE are not exceptionally difficult,
but if you are even the least bit skittish about numbers you’ll have a harder
time working the problems.
This chapter will familiarize you with all the basics you need to know about
numbers and how to work with them. If you’re an arithmophobe or haven’t
used math in a while, take it slowly and make sure you’re comfortable with
this chapter before moving onto the succeeding ones.
You may be a little rusty
when it comes to working
with numbers, but, with a
little practice, you’ll
be surprised at how
quickly you’ll become
comfortable again.
GRE MATH VOCABULARY
Quick—what’s an integer? Is 0 even or odd? How many even prime numbers
are there?
Before we go through our techniques for specific types of math problems,
we’ll acquaint ourselves with some basic vocabulary and properties of
numbers. The GRE loves to test your knowledge of integers, fractions,
decimals, and all those other concepts you probably learned years ago. Make
sure you’re comfortable with the topics in this chapter before moving on.
Even if you feel fairly at ease with number concepts, you should still work
through this chapter. ETS is very good at coming up with questions that
require you to know ideas forwards and backwards.
The math terms we will review in this section are very simple, but that
doesn’t mean they’re not important. Every GRE math question uses simple
terms, rules, and definitions. You absolutely need to know this math
“vocabulary.” Don’t worry; we will cover only the math terms that you must
know for the GRE.
Learn your math
vocabulary!
Digits
Digit refers to the numbers that make up other numbers. There are 10 digits:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and every number is made up of one or more digits.
For example, the number 10,897 has five digits: 1, 0, 8, 9, and 7. Each of the
digits in a number has its own name, which is designated by a place value. In
the number 10,897
•
7 is the ones or units digit.
•
9 is the tens digit.
•
8 is the hundreds digit.
•
0 is the thousands digit.
•
1 is the ten-thousands digit.
Numbers
A number is made up of either a digit or a collection of digits. There are, of
course, an infinite number of numbers. Basically, any combination of digits
you can imagine is a number, which includes 0, negative numbers, fractions
and decimals, and even weird numbers such as
.
GRE problems like to try
to trip you up on the
difference between a
number and an integer.
Integers
The integers are the numbers that have no fractional or decimal part, such as
−6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6, and so on.
Notice that fractions, such as , are not integers.
Remember that the number zero is an integer! The values of positive integers
increase as they move away from 0 (6 is greater than 5); the values of
negative integers decrease as they move away from zero (−6 is less than −5).
Remember: Fractions are
NOT integers.
PROPERTIES OF NUMBERS AND INTEGERS
Now that you’ve learned the proper names for various types of numbers, let’s
look at properties of numbers and integers.
Positive or Negative
Numbers can be positive or negative. Negative numbers are less than zero,
while positive numbers are greater than zero. Zero itself is neither positive nor
negative—all other numbers are either positive or negative.
Even or Odd
Only integers possess the property of being even or odd. Fractions, decimals,
and other non-integers cannot be described as even or odd. Integers that are
even are those that are divisible by 2; odd integers are those integers that are
not divisible by 2. Put another way, even integers have a remainder of 0 when
divided by 2 while odd integers have a remainder of 1 when divided by 2.
•
Here are some even integers: −4, −2, 0, 2, 4, 6, 8, 10.
•
Here are some odd integers: −3, −1, 1, 3, 5, 7, 9, 11.
Zero
Zero is a special little number. It is an integer, but it is neither positive nor
negative. However, try to remember these facts about zero:
•
0 is even.
•
0 plus any other number is equal to that other number.
•
0 multiplied by any other number is equal to 0.
•
You cannot divide by 0.
Zero has a number of
special properties that are
tested frequently on the
GRE. Technically, zero is a
multiple of every number,
but this fact is rarely
tested on the GRE.
Keep in Mind
•
Fractions are neither even nor odd.
•
Any integer is even if its units digit is even; any integer is odd if
its units digit is odd.
•
The results of adding and multiplying odd and even integers are
as follows:
even + even = even
odd + odd = even
even + odd = odd
even × even = even
odd × odd = odd
even × odd = even
If you have trouble remembering some of these rules for odd and even, don’t
worry. As long as you remember that there are rules, you can always figure
them out by plugging in numbers. Let’s say you forget what happens when an
odd number is multiplied by an odd number. Just pick two odd numbers, say 3
and 5, and multiply them. 3 × 5 = 15. Now you know: odd × odd = odd.
Be careful: Don’t confuse
odd and even with
positive and negative!
Consecutive Integers
Consecutive integers are integers listed in order of value without any
integers missing in between them. Here are some examples:
•
0, 1, 2, 3, 4, 5
•
−6, −5, −4, −3, −2, −1, 0
•
−3, −2, −1, 0, 1, 2, 3
By the way, fractions and decimals cannot be consecutive, only integers can
be consecutive. However, you can have different types of consecutive
integers. For example consecutive even integers could be 2, 4, 6, 8, 10.
Consecutive multiples of four could be 4, 8, 12, 16.
Absolute Value
The absolute value of a number is equal to its distance from 0 on the number
line, which means that the absolute value of any number is always positive,
whether the number itself is positive or negative. The symbol for absolute
value is a set of double lines:
FACTORS, MULTIPLES, AND DIVISIBILITY
Now let’s look at some ways that integers are related to each other.
Factors
A factor of a particular integer is a number that will divide evenly into the
integer in question. For example, 1, 2, 3, 4, 6, and 12 are all factors of 12
because each number divides evenly into 12. In order to find all the factors of
a particular integer, write down the factors systematically in pairs of integers
that, when multiplied together, make 12, starting with 1 and the integer itself:
•
1 and 12
•
2 and 6
•
3 and 4
If you always start with 1 and the integer itself and work your way up, you’ll
make sure you get them all.
Multiples
The multiples of an integer are all the integers for which the original integer
is a factor. For example, the multiples of 8 are all the integers of which 8 is a
factor: 8, 16, 24, 32, 40, and so on. Note that there are an infinite number of
multiples for any given number. Also, zero is a multiple of every number,
although this concept is rarely tested on the GRE.
There are only a few
factors of any number;
there are many multiples
of any number.
Prime Numbers
A prime number is an integer that only has two factors: itself and one. Thus,
37 is prime because the only integers that divide evenly into it are 1 and 37,
while 10 is not prime because its factors are 1, 2, 5, and 10.
Here is a list of all the prime numbers that are less than 30: 2, 3, 5, 7, 11, 13,
17, 19, 23, 29.
Here are some other facts about primes that are important to remember:
•
0 is not a prime number.
•
1 is not a prime number.
•
2 is the only even prime number.
•
Prime numbers are positive integers. There’s no such thing as a
negative prime number or a prime fraction.
1 is not prime!
Divisibility
An integer is always divisible by its factors. If you’re not sure if one integer is
divisible by another, a surefire way to find out is to use the calculator.
However, there are also certain rules you can use to determine whether one
integer is a factor of another.
•
An integer is divisible by 2 if its units digit is divisible by 2. For
example, we know just by glancing at it that 598,447,896 is
divisible by 2, because the units digit, 6, is divisible by 2.
•
An integer is divisible by 3 if the sum of its digits is divisible by 3.
For example, we know that 2,145 is divisible by 3 because 2 + 1 +
4 + 5 = 12, and 12 is divisible by 3.
•
An integer is divisible by 4 if its last two digits form a number
that’s divisible by 4. For example, 712 is divisible by 4 because 12
is divisible by 4.
•
An integer is divisible by 5 if its units digit is either 0 or 5. For
example, 23,645 is divisible by 5 because its units digit is 5.
•
An integer is divisible by 6 if it’s divisible by both 2 and 3. For
example, 4,290 is divisible by 6 because it is divisible by 2 (it’s
even) and by 3 (4 + 2 + 9 = 15, which is divisible by 3).
•
An integer is divisible by 8 if its last three digits form a number
that’s divisible by 8. For example, 11,640 is divisible by 8 because
640 is divisible by 8.
•
An integer is divisible by 9 if the sum of its digits is divisible by 9.
For example, 1,881 is divisible by 9 because 1 + 8 + 8 + 1 = 18,
which is divisible by 9.
•
An integer is divisible by 10 if its units digit is 0. For example,
1,590 is divisible by 10 because its units digit is 0.
Remainders
If one integer is not divisible by another—meaning that the second integer is
not a factor of the first number—you’ll have an integer left over when you
divide. This left-over integer is called a remainder; you probably remember
working with remainders in grade school.
For example, when 4 is divided by 2, there’s nothing left over so there’s no
remainder. In other words, 4 is divisible by 2. You could also say that the
remainder is 0.
On the other hand, 5 divided by 2 is 2, with 1 left over; 1 is the remainder.
Thirteen divided by 8 is 1, with 5 left over as the remainder.
If a question asks about
a remainder, don’t use
the calculator. Use long
division.
Note that remainders are always less than the number that you are dividing
by. For example, the remainder when 13 is divided by 7 is 6. What happens if
you divide 14, the next integer, by 7? The remainder is 0.
Here’s one more thing to know about remainders. What’s the remainder when
5 is divided by 6? The remainder is 5 because 5 can be divided by 6 zero
times and the amount that remains is 5. When the positive integer you are
dividing by is greater than the integer being divided, the remainder will
always be the number being divided.
MORE MATH VOCABULARY
In a way, the Math section is almost as much of a vocabulary test as the
Verbal section. Below, you’ll find some more standard terms that you should
commit to memory before you do any practice problems.
Term
Meaning
sum
difference
product
quotient
divisor
numerator
denominator
consecutive
terms
the result of addition
the result of subtraction
the result of multiplication
the result of division
the number you divide by
the top number in a fraction
the bottom number in a fraction
in order from least to greatest
the numbers and expressions used in an
equation
BASIC OPERATIONS WITH NUMBERS
Now that you’ve learned about numbers and their properties, you’re ready to
begin working with them. As we mentioned above, there are four basic
operations you can perform on a number: addition, subtraction,
multiplication, and division.
Order of Operations
When you work with numbers you can’t just perform the four operations in
any way you please. Instead, there are some very specific rules to follow,
which are commonly referred to as the order of operations.
It is absolutely necessary that you perform these operations in exactly the
right order. In many cases, the correct order will be apparent from the way the
problem is written. In cases in which the correct order is not apparent, you
need to remember the following mnemonic.
Please Excuse My Dear Aunt Sally, or PEMDAS.
What does PEMDAS stand for?
P stands for “parentheses.” Solve anything in parentheses first.
E stands for “exponents.” Solve exponents next. (We’ll review exponents
soon.)
M stands for “multiplication” and D stands for “division.” The arrow
indicates that you do all the multiplication and division together in the same
step, going from left to right.
A stands for “addition” and S stands for “subtraction.” Again, the arrow
indicates that you do all the addition and subtraction together in one step,
from left to right.
Let’s look at an example:
12 + 4(2 + 1)2 ÷ 6 − 7 =
Here’s How to Crack It
Start by doing all the math inside the parentheses. 2 + 1 = 3. Now the problem
looks like this:
12 + 4(3)2 ÷ 6 − 7 =
Next we have to apply the exponent. 32 = 9. Now this is what we have:
12 + 4(9) ÷ 6 − 7 =
Now we do multiplication and division from left to right. 4 × 9 = 36, and 36 ÷
6 = 6, which gives us
12 + 6 − 7 =
Finally, we do the addition and subtraction from left to right. 12 + 6 = 18, and
18 − 7 = 11. Therefore,
12 + 4(2 + 1)2 ÷ 6 − 7 = 11
Multiplication and Division
When multiplying or dividing, keep the following rules in mind:
•
positive × positive = positive
2×2=4
•
negative × negative = positive
−2 × −2 = 4
•
positive × negative = negative
2 × −2 = −4
•
positive ÷ positive = positive
8÷2=4
•
negative ÷ negative = positive
−8 ÷ −2 = 4
•
positive ÷ negative = negative
8 ÷ −2 = −4
Before taking the GRE, you should have your times tables memorized from 1
through 15. It will be a tremendous advantage if you can quickly and
confidently recall that 7 × 12 = 84, for example.
It seems like a small thing,
but memorizing your times
tables will really help you
on test day.
FRACTIONS, DECIMALS, AND PERCENTAGES
One of the ways ETS tests your fundamental math abilities is through
Fractions, Decimals, and Percents. So let’s expand our conversation on math
fundamentals to include these concepts.
Fractions
A fraction expresses the number of parts out of a whole. In the fraction , for
instance, the top part, or numerator, tells us that we have 2 parts, while the
bottom part of the fraction, the denominator, indicates that the whole, or
total, consists of 3 parts. We use fractions whenever we’re dealing with a
quantity that’s between two whole numbers.
Notice that the fraction bar is simply another way of expressing division.
Thus, the fraction
is just expressing the idea of “2 divided by 3.”
Fractions are important on
the GRE. Make sure you’re
comfortable with them.
Reducing and Expanding Fractions
Fractions express a relationship between numbers, not actual amounts. For
example, saying that you did
of your homework expresses the same idea
whether you had 10 pages of homework to do and you’ve done 5 pages, or
you had 50 pages to do and you’ve done 25 pages. This concept is important
because on the GRE you’ll frequently have to reduce or expand fractions.
To reduce a fraction, express the numerator and denominator as the products
of their factors. Then cross out, or “cancel,” factors that are common to both
the numerator and denominator. Here’s an example:
You can achieve the same result by dividing the numerator and denominator
by the factors that are common to both. In the example you just saw, you
might realize that 4 is a factor of both the numerator and the denominator.
That is, both the numerator and the denominator can be divided evenly
(without a remainder) by 4. Doing this yields the much more manageable
fraction .
When you confront GRE math problems that involve fractions with great
numbers, always reduce them before doing anything else.
Look at each of the following fractions:
What do you notice about each of these fractions? They all express the same
information! Each of these fractions expresses the relationship of “1 part out
of 4 total parts.”
Adding and Subtracting Fractions
Adding and subtracting fractions that have a common denominator is easy—
you just add the numerators and put the sum over the common denominator.
Here’s an example:
Why Bother?
You may be wondering why, if the GRE allows the use of a calculator,
you should bother learning how to add or subtract fractions or to
reduce them or even know any of the topics covered in the next few
pages. While it’s true that you can use a calculator for these tasks, for
many problems it’s actually slower to do the math with the calculator
than without. Scoring well on the GRE Math section requires a fairly
strong grasp of the basic relationships among numbers, fractions,
percents, and so on, so it’s in your best interest to really understand
these concepts rather than to rely on your calculator to get you
through the question. In fact, if you put in the work now, you’ll be
surprised at how easy some of the problems become, especially when
you don’t have to refer constantly to the calculator to perform basic
operations.
In order to add or subtract fractions that have different denominators, you
need to start by finding a common denominator. You may remember your
teachers from grade school imploring you to find the “lowest common
denominator.” Actually, any common denominator will do, so find whichever
one you find most comfortable working with.
Here, we expanded the fraction
into the equivalent fraction
by
multiplying both the numerator and denominator by 3. Similarly, we
converted
to
by multiplying both denominator and numerator by 2.
This left us with two fractions that had the same denominator, which meant
that we could simply subtract their numerators.
When adding and subtracting fractions, you can also use a technique we call
the Bowtie. The Bowtie method accomplishes exactly what we just did in one
fell swoop. To use the Bowtie, first multiply the denominators of each
fraction. This gives you a common denominator. Then multiply the
denominator of each fraction by the numerator of the other fraction. Take
these numbers and add or subtract them—depending on what the question
asks you to do—to get the numerator of the answer. Then reduce if necessary.
and
The Bowtie method is a
convenient shortcut to use
when you’re adding and
subtracting fractions.
Multiplying Fractions
Multiplying fractions is relatively straightforward when compared to addition
or subtraction. To successfully multiply fractions, multiply the first numerator
by the second numerator and the first denominator by the second
denominator. Here’s an example:
When multiplying fractions, you can make your life easier by reducing before
you multiply. Do this once again by dividing out common factors.
Also remember that when you’re multiplying fractions, you can even reduce
diagonally; as long as you’re working with a numerator and a denominator of
opposite fractions, they don’t have to be in the same fraction. So you end up
with:
Of course, you get the same answer no matter what method you use, so attack
fractions in whatever fashion you find easiest.
Multiplying fractions
is a snap: Just multiply
straight across, numerator
times numerator and
denominator times
denominator.
Dividing Fractions
Dividing fractions is just like multiplying fractions, with one crucial
difference: Before you multiply, you have to to find the reciprocal of the
second fraction. To do this, all you need to do is flip the fraction upside down!
Put the denominator on top of the numerator and then multiply just like
before. In some cases, you can also reduce before you multiply. Here’s an
example:
ETS tests problems that involve fractions which have numerators or
denominators that are themselves fractions. These problems might look
intimidating, but if you’re careful, you won’t have any trouble with them. All
you have to do is remember what we said about a fraction being shorthand for
division. Always rewrite the expression horizontally. Here’s an example:
Comparing Fractions
Sometimes ETS will test your ability to compare two fractions to decide
which is greatest. These are typically found on quant comp questions. There
are a couple of ways to accomplish this. One is to find equivalent fractions
that have a common denominator. If the fraction is fairly simple this is a good
strategy, but oftentimes the common denominator may be hard to find or work
with.
If the denominator is hard to find or work with, you can use a variant of the
Bowtie technique. In this variant, you don’t have to multiply the
denominators together; instead, just multiply the denominators and the
numerators. The fraction with the greater product in its numerator is the
greater fraction. Let’s say we had to compare the following fractions:
Multiplying the first denominator by the second numerator yields 49. This
means the numerator of the second fraction
is 49. Multiplying the
second denominator by the first numerator gives you 36, which means the
first fraction has a numerator of 36. Since 49 is greater than 36,
is greater
than .
You can also use the
calculator feature to
change the fractions
into decimals.
Comparing More Than Two Fractions
You may also be asked to compare more than two fractions. On these types of
problems, don’t waste time trying to find a common denominator for all of
them. Simply use the Bowtie to compare two of the fractions at a time.
Here’s an example:
Which of the following statements is true?
Here’s How to Crack It
As you can see, it would be a nightmare to try to find common denominators
for all these fractions, so instead we’ll use the Bowtie method. Simply
multiply the denominators and numerators of a pair of fractions and note the
results. For example, to check answer choice (A), we first multiply 8 and 2,
which gives us a numerator of 16 for the fraction . But multiplying 9 and 3
gives us a numerator of 27 for the first fraction. This means that
is greater
than , and we can eliminate choice (A), because the first part of it is wrong.
Here’s how the rest of the choices shape up:
Compare
and
;
is greater. Eliminate (B).
These fractions are in order.
is greater than . Eliminate (D).
is greater than . Eliminate (E).
The answer is (C).
Converting Mixed Numbers into Fractions
A mixed number is a number that is represented as an integer and a fraction,
such as 2 . In most cases on the GRE, you should get rid of mixed fractions
by converting them to improper fractions. How do you do this? By
multiplying the denominator of the fraction by the integer, then adding that
result to the numerator, and then putting the whole thing over the
denominator. In other words, for the fraction above we would get
or
.
The result, , is equivalent to 2 . The only difference is that
is easier to
work with in math problems. Also, answer choices are usually not given in
the form of mixed numbers.
Improper fractions have a
numerator that is greater
than the denominator.
When you convert mixed
numbers, you’ll get
an improper fraction as
the result.
Decimals
Decimals are just fractions in disguise. Basically, decimals and fractions are
two different ways of expressing the same thing. Every decimal can be
written as a fraction, and every fraction can be written as a decimal. For
example, the decimal 0.35 can be written as the fraction
: These two
numbers, 0.35 and
, have the same value.
To turn a fraction into its decimal equivalent, all you have to do is divide the
numerator by the denominator. Here, for example, is how you would find the
decimal equivalent of :
Try this problem:
+ =x
y=3
Quantity A
Quantity B
4
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
Begin this quant comp question by solving for x. The common denominator is
easy to find, as it is 15, so adjust the fractions to have the denominator of 15.
The problem gives the value of y so now solve for Quantity A. Quantity A is
which equals
. Now compare this to Quantity B. Dividing 45
by 11 yields a result slightly greater than 4, which means that Quantity A is
greater than Quantity B and the correct answer is (A).
Comparing Decimals
Which is greater: 0.00099 or 0.001? ETS loves this sort of problem. You’ll
never go wrong, though, if you follow these easy steps.
•
Line up the numbers by their decimal points.
•
Fill in the missing zeros.
Here’s how to answer the question we just asked. First, line up the two
numbers by their decimal points.
0.00099
0.001
Now fill in the missing zeros.
0.00099
0.00100
Can you tell which number is greater? Of course you can. 0.00100 is greater
than 0.00099, because 100 is greater than 99.
Digits and Decimals
Sometimes ETS will ask you questions about digits that fall after the decimal
point as well. Suppose you have the number 0.584.
•
0 is the units digit.
•
5 is the tenths digit.
•
8 is the hundredths digit.
•
4 is the thousandths digit.
Percentages
A percentage is just a special type of fraction, one that always has 100 as the
denominator. Percent literally means “per 100” or “out of 100” or “divided by
100.” If your best friend finds a dollar and gives you 50¢, your friend has
given you 50¢ out of 100, or
of a dollar, or 50 percent of the dollar. To
convert fractions to percentages, just expand the fraction so it has a
denominator of 100:
= 60%
Another way to
convert a fraction into
a percentage is to
divide the numerator
by the denominator
and multiply the result
by 100. So,
=3÷5=
0.6 × 100 = 60%.
For the GRE, you should memorize the following percentage-decimalfraction equivalents. Use these friendly fractions and percentages to eliminate
answer choices.
Converting Decimals to Percentages
In order to convert decimals to percentages, just move the decimal point two
places to the right. For example, 0.8 turns into 80 percent, 0.25 into 25
percent, 0.5 into 50 percent, and 1 into 100 percent.
Translation
One of the best ways to handle percentages in word problems is to know how
to translate them into an equation that you can manipulate. Use the following
table to help you translate percentage word problems into equations you can
work with.
These translations apply to
any word problem, not just
percent problems.
Here’s an example:
56 is what percent of 80 ?
66%
70%
75%
80%
142%
Here’s How to Crack It
To solve this problem, let’s translate the question and then solve for the
variable. So, “56 is what percent of 80,” in math speak, is equal to
56=
(80)
56=
Don’t forget to reduce the fraction: 56 = x.
Now multiply both sides of the equation by the reciprocal, .
(56) = x
=x
= x = 70
The correct answer is (B), 70%.
Let’s try a quant comp example.
5 is r percent of 25
s is 25 percent of 60
Quantity A
Quantity B
r
s
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
First translate the first statement.
5=
(25)
5=
5=
(4)(5) =
(4)
20 = r
That takes care of Quantity A. Now translate the second statement.
s=
(60)
s = (60)
s = 15
So Quantity A is greater than Quantity B. The answer is (A).
Percentage Increase/Decrease
Rather than asking for percents, ETS typically will test your knowledge by
asking for percent change. Percent change is the percentage by which
something has increased or decreased. To find percent change, use the
following formula.
Percent Change =
× 100
On percent increase
problems, the original is
always the smaller number.
On percent decrease
problems, the original is
the larger number.
When presented with a percent change problem, you will typically be given
two numbers. The “difference” is the result when the lesser number is
subtracted from the greater number. The “original” is whichever number you
started with. If the question asks you to find a percent increase, then the
original number is the lesser number. If the question asks you to find a
percent decrease, then the original number is the greater number.
On the GRE, a percent change will not be stated as a negative number.
Instead, the problem will ask for a percent decrease. So, if something declined
by 50%, the problem will ask for a percent decrease and the answer will be
stated as 50%. Note that when you use the percent change formula, you
always subtract the lesser number from the greater number to find the
difference. Doing so ensures that you get a positive result.
Here’s an example.
During a certain three-month period, Vandelay Industries reported a $3,500 profit.
If, over the next three-month period, Vandelay Industries reported $6,000 profit for
those months, by approximately what percent did Vandelay Industries’ profit
increase?
25%
32%
42%
55%
70%
Here’s How to Crack It
Let’s use the percent change formula we just learned. The first step is to find
the difference between the two numbers. The initial profit was $3,500 and the
final profit is $6,000. The difference between these two numbers is 6,000 −
3,500 = 2,500. Next, we need to divide this number by the original, or
starting, value.
One way to help you figure out what value to use as the original value is to
check to see whether you’re dealing with a percent increase or a percent
decrease question. Remember that on a percent increase question, you should
always use the lesser of the two numbers as the denominator and on a percent
decrease question you need to use the greater of the two numbers as the
denominator. Because the question asks to find the percent increase, the
number we want to use for our denominator is 3,500. The percent increase
fraction looks like this:
. This can be reduced to
by dividing by 100,
and reduced even further by dividing by 5. The reduced fraction is , which is
approximately 70% (remember that the fraction bar means divide, so if you
divide 5 by 7, you’ll get 0.71). Thus, (E) is the correct answer.
Here’s another question.
The table above shows the original price and the sale price for six different models
of cars. For which car models is the percent decrease at least 25% ?
Indicate all such models.
A
B
C
D
E
F
Here’s How to Crack It
The task of this question is to identify a 25% or greater percent decrease
between the two prices for the different car models. Use the percent change
formula for all of the models to solve this question. Start with model A. Using
the calculator, subtract 9,500 from 12,000 to get 2,500. This is the difference.
Divide it by the original, 12,000, to get about 0.2, which when multiplied by
100 is 20%. Since 20% is less than 25%, eliminate (A). Try the next one.
16,000 − 13,000 = 3,000. Divide 3,000 by 16,000. The result is less than 25%,
so eliminate (B). Repeat this process for each of the answer choices. Choices
(C), (D), and (F) are the correct answers.
A FEW LAWS
These two basic laws are not necessary for success on the GRE, so if you
have trouble with them, don’t worry too much. However, ETS likes to use
these laws to make certain math problems more difficult. If you’re
comfortable with these two laws, you’ll be able to simplify problems using
them, so it’s definitely worth it to use them.
Associative Laws
There are two associative laws—one for addition and one for multiplication.
For the sake of simplicity, we’ve lumped them together.
Here’s what you need to know:
When you are adding or multiplying a series of numbers, you can
regroup the numbers in any way you’d like.
Here are some examples:
4 + (5 + 8) = (4 + 5) + 8 = (4 + 8) + 5
(a + b) + (c + d) = a + (b + c + d)
4 × (5 × 8) = (4 × 5) × 8 = (4 × 8) × 5
(ab)(cd) = a(bcd)
Distributive Law
This is often tested on the GRE. Here’s what it looks like:
a(b + c) = ab + ac
a(b – c) = ab – ac
Here’s an example:
12(66) + 12(24) = ?
Here’s How to Crack It
This is in the same form as ab + ac. Using the distributive law, this must
equal 12(66 + 24), or 12(90) = 1,080.
Math Fundamentals Drill
Test your new skills and check your answers in Part V.
1 of 10
If a prime number, p, is squared and the result is added to the next prime number greater than p, which
of the following integers could be the resulting sum?
Indicate all such integers.
3
4
7
14
58
60
65
69
2 of 10
A bookstore will only order books that come in complete cases. Each case has 150 books and costs
$1,757.
Quantity A
Quantity B
The number of books that can
be ordered for $10,550
The number of books that can
be ordered for $12,290
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
3 of 10
If the product of two distinct integers is 91, then which of the following could be the sum of the two
integers?
Indicate all such sums.
−92
−91
7
13
20
4 of 10
Which of the following is the digit for the sum of all of the distinct prime integers less than 20 ?
4
5
6
7
8
5 of 10
During a sale, a store decreases the prices on all of its scarves by 25 to 50 percent. If all of the scarves in
the store were originally priced at $20, which of the following prices could be the sale price of a scarf?
Indicate all such prices.
$8
$10
$12
$14
$16
6 of 10
−2, 3, −5, −2, 3, −5, −2, 3, −5,…
In the sequence above, the first 3 terms repeat without end. What is the product of the 81st term through
the 85th term?
7 of 10
Quantity A
Quantity B
2x + 8y
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
8 of 10
Quantity A
Quantity B
The greatest number of
consecutive nonnegative
integers which have a sum less
than 22
6
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
9 of 10
If x is the remainder when a multiple of 4 is divided by 6, and y is the remainder when a multiple of 2 is
divided by 3, what is the greatest possible value of x + y ?
2
3
5
6
9
10 of 10
12−
− 8 × 3=
−46
−30
−18
−6
−2
Summary
Familiarity with the basic math concepts on the GRE is essential to
achieving a great score.
Digits are the numbers that make up other numbers, which are
collections of digits, and those other numbers are determined by the
place value of the digits.
Integers are numbers with no fractional part (such as −6, −1, 1, 10, etc.)
and can be positive or negative, and even or odd.
Zero is an integer that is neither positive nor negative.
Consecutive integers are integers listed in some sort of order.
The absolute value of a number is that number’s distance away from
zero on a number line.
A factor of a particular integer is an integer that divides evenly into that
integer.
A multiple of a number is a number that has the original number as a
factor.
Prime numbers only have two factors: 1 and the number itself.
Divisibility is the ability for one number to be divided into another
number with a result that is an integer. If a number divided by another
number and the result is not an integer, the amount that is leftover is
called the remainder.
Always follow the order of operations when working a math problem.
Fractions, decimals, and percents are all ways of expressing parts of
integers and can be manipulated and compared.
The associative and distributive laws are useful ways to group and
regroup numbers.
Chapter 11
Algebra (And When to Use It)
The basics for math on the GRE are often used in the context of algebra.
While comfort with algebraic operations is a good skill to have, plugging in
numbers in lieu of doing the algebra is often a much faster way of getting the
correct answer. This chapter provides an introduction to the strategies we call
Plugging In and Plugging In The Answers, as well as explains how to deal
with exponents and square roots, and how to manipulate equations,
inequalities, quadratic equations, and simultaneous equations.
PLUGGING IN
Many of the hardest questions you might encounter on the GRE involve
algebra. Algebra questions are generally difficult for two reasons. First, they
are often complicated, multistep problems. Second, ETS studies the types of
mistakes that people make when they solve questions using algebra. They
generate wrong answers for the questions based on these common algebraic
errors. So, if you aren’t careful, you can make an algebraic mistake and still
find your answer among the choices.
If you are one of the many students who take the GRE and struggle with
Algebra, you’re in luck. Plugging In is a strategy that will turn even the
hardest, messiest GRE algebra problem into an arithmetic problem.
Let’s look at an example of how Plugging In can make a seemingly messy
algebra problem much easier to work with.
Dale gives Miranda x bottles of water. He gives Marcella two fewer bottles of
water than he gives to Miranda and he gives Mary three more bottles of water than
he gives to Marcella. How many bottles of water did Dale give to Miranda,
Marcella and Mary, in terms of x ?
3x − 1
3x
3x + 1
3x + 2
x−2
Why Plug In?
Plugging In is a powerful tool that can greatly enhance your math
score, but you may be wondering why you should Plug In when
algebra works just fine. Here’s why:
Plugging In converts algebra problems into arithmetic problems. No
matter how good you are at algebra, you’re better at arithmetic. Why?
Because you use arithmetic every day, every time you go to a store,
balance your checkbook, or tip a waiter. Chances are you rarely use
algebra in your day-to-day activities.
Plugging In is oftentimes more accurate than algebra. When you plug
in real numbers, you make the problems concrete rather than abstract.
Once you’re working with real numbers, it’s easier to notice when and
where you’ve messed up a calculation. It’s much harder to see where
you went wrong (or to even know you’ve done something wrong)
when you’re staring at a bunch of x’s and y’s.
The GRE allows the use of a calculator. A calculator can do arithmetic
but it can’t do algebra, so Plugging In allows you to take advantage of
the calculator function.
ETS expects its students to attack the problems algebraically and
many of the tricks and the traps built into the problem are designed to
catch students who use algebra. By Plugging In, you’ll avoid these
pitfalls.
As you can see, there are a number of excellent reasons for Plugging
In. Mastering this technique can have a significant impact on your
score.
Here’s How to Crack It
This problem can definitely be solved using algebra. However, the use of
Plugging In makes this problem much easier to solve. The problem has one
variable in it, x, so start plugging in by picking a number for x. An easy
number to use would be 10, so use your scratch paper and write down x = 10.
Now read the problem again and follow the directions, only this time do the
arithmetic instead of the algebra on the scratch paper. So, Miranda gets 10
bottles of water. The problem then states that Marcella gets two fewer bottles
of water than Miranda, so Marcella gets 8 bottles. Next, Mary gets three more
bottles than Marcella, so Mary gets 11 bottles. That’s a total of 10 + 8 + 11 =
29 bottles of water. The problem asks how many bottles of water Dale gave to
Miranda, Marcella, and Mary, so the answer to the question is 29 bottles of
water. This is the target answer, which should always be circled on the scratch
paper so you don’t forget it. Now plug in 10 for the variable x in all the
answer choices and see which answer choice equals 29. Be sure to check all
five answer choices.
(A)
(B)
(C)
(D)
(E)
3(10) − 1 = 29
3(10) = 30
3(10) + 1 = 31
3(10) + 2 = 32
10 − 2 = 8
Looks good!
Nope
Nope
Nope
Nope
The correct answer to this question is (A), and if you successfully completed
the algebra you would have gotten the same answer. Pretty easy compared to
the algebra, huh?
As you can see, Plugging In turned this algebra problem into an arithmetic
problem. The best news is that you can solve any problem with variables by
using Plugging In.
Here are the steps:
Step 1:
Recognize the opportunity. See variables in the problem
and answer choices? Get ready to Plug In. The minute you
see variables in a question or answer choices, you should
start thinking about opportunities to Plug In.
Step 2:
Set up the scratch paper. Plugging In is designed to make
your life easier. Why make it harder again by trying to
solve problems in your head? You are not saving any
notable amount of time by trying to work out all the math
without writing it down, so use the scratch paper. Even if it
seems like an easy question of translating a word problem
into an algebraic equation, remember that there are trap
answer choices. Whenever you recognize the opportunity
to Plug In, set up the scratch paper by writing answer
choices (A) through (E) down before you start to solve.
Plugging In
This technique can be
achieved by following
these five simple steps.
Plugging in numbers in
place of variables can
make algebra problems
much easier to solve.
Step 3:
Plug In. If the question asks for “x apples,” come up with
a number for x. The goal here is to make your life easier,
so plugging in numbers such as 2, 3, 5, 10, 100 are all
good strategies. However, for the first attempt at Plugging
In on any given problem, avoid the numbers 1 or 0. These
numbers can oftentimes create a situation where more than
one answer choice produces the target answer. If you plug
in a number and the math starts getting difficult (for
example, you start getting fractions or negative numbers),
don’t be afraid to just change the number you plug in.
Step 4:
Solve for the Target. The Target is the value the problem
asks you to solve for. Remember to always circle the
Target so you don’t forget what it is you are solving for.
Step 5:
Check all of the answer choices. Anywhere you see a
variable, plug in the number you have written down for
that variable and do the arithmetic. The correct answer is
the one that matches the Target. If more than one answer
matches the Target, just plug in a different number for the
variables and test the answer choice you were unable to
eliminate with the original number.
Can I Just Plug In Anything?
You can plug in any numbers you like, as long as they’re consistent with any
restrictions stated in the problem, but it’s more effective if you use easy
numbers. What makes a number easy? That depends on the problem, but in
most cases, lesser numbers are easier to work with than greater numbers.
Usually, it’s best to start with a lesser number, such as 2 for example. Avoid
the numbers 0 and 1; both 0 and 1 have special properties, which you’ll hear
more about later. You want to avoid these numbers because they will often
make more than one answer choice match the target. For example, if we plug
in 0 for a variable such as x, then the answers 2x, 3x, and 5x would all equal 0.
Also, try to avoid plugging in any numbers that are repeats of numbers that
show up a lot in the question or answer choices. If you can avoid plugging in
0, 1, or repeat numbers, you can oftentimes avoid situations that may make
you have to Plug In again.
Plug in numbers that make
the calculations EASY.
Good Numbers Make Life Easier
However, numbers of lesser value aren’t always the best choices for Plugging
In. What makes a number good to work with depends on the context of the
problem, so be on the lookout for clues to help choose the numbers you are
going to use to Plug In. For instance, in a problem involved percentages the
numbers 10 and 100 are good numbers to use. In a problem that involves
minutes or seconds any multiple or factor of 60, such as 30 or 120 are often
good choices.
Plug in real numbers for
variables to turn algebra
into arithmetic!
Let’s use the Plugging In steps from above to work through the following
problem.
Mara has six more than twice as many apples as Robert and half as many apples as
Sheila. If Robert has x apples, then, in terms of x, how many apples do Mara,
Robert, and Sheila have combined?
2x + 6
2x + 9
3x + 12
4x + 9
7x + 18
On the GRE, Plugging In
is often more accurate,
and easier, than doing the
algebra.
Here’s How to Crack It
Step 1:
Recognize the opportunity. Look at the question. There
is the variable x in the question stem and the answer
choices. This is a clear indication to start thinking about
Plugging In.
Step 2:
Set up the scratch paper. Keep yourself organized by
listing out answer choices (A) through (E) on the scratch
paper. Leave some space to work the problem.
Step 3:
Plug In. Plug in a good number. The problem states that
Robert has x apples, and doesn’t indicate that the number
of apples needs to be anything specific, so choose an easy
number such as x = 4.
Step 4:
Solve for the Target. Now use x = 4 to read the problem
again and solve for the target. The problem states that
“Mara has six more than twice as many apples as Robert.”
If Robert has 4 apples, then Mara must have 14. Next, the
problem states that Mara has “half as many apples as
Sheila.” That means that Sheila must have 28 apples. The
question asks for the number of apples that Robert, Sheila,
and Mara have combined so add 4 + 14 + 28 = 46 apples.
This is the target number, so circle it.
Step 5:
Check all of the answer choices. Plug in x = 4 for all of
the variables in the answer choices and use the scratch
paper to solve them, eliminating any answer choice that
does not equal 46.
(A) 2(4) + 6 = 14—This is not 46, so eliminate it.
(B) 2(4) + 9 = 17—Eliminate this too.
(C) 3(4) + 12 = 24—Also not 46, so eliminate this.
(D) 4(4) + 9 = 25—This is still not 46, so eliminate this
as well.
(E) 7(4) + 18 = 46—Bingo! This is the correct answer.
On the GRE, plug in for variables in the question and answer choices.
Remember to plug in numbers that will be easy to work with based on the
problem, as some numbers can end up causing more trouble than they are
worth.
Always be on the lookout
for variables and if you see
them, get ready to Plug In!
When Plugging In, follow these rules:
1. Avoid plugging in 0 or 1. These numbers, while easy to work
with, have special properties.
2. Avoid plugging in numbers that are already in the problem;
this often leads to more than one answer matching your target.
3. Avoid plugging in the same number for multiple variables.
For example, if a problem has x, y, and z in it, pick three
different numbers to plug in for the three variables.
4. Avoid plugging in conversion numbers. For example, don’t
use 60 for a problem involving hours, minutes, or seconds.
Finally, Plugging In is a powerful tool, but you must remember to always
check all five answer choices when you Plug In. In certain cases, two
answer choices can yield the same target. This doesn’t necessarily mean you
did anything wrong; you just hit some bad luck. When this happens, just plug
in different numbers, solve for a new target, and recheck the answer choices
that worked the first time.
PLUGGING IN THE ANSWERS (PITA)
Some questions may not have variables in them but will try to tempt you into
using algebra to solve them. We call these Plugging In the Answers questions,
or PITA for short. These are almost always difficult problems but once you
recognize the opportunity to PITA, these questions turn into simple arithmetic
questions. In fact, the hardest part of these problems is often identifying them
as opportunities for PITA. The beauty of these questions is that they take
advantage of one of the inherent limitations of a multiple-choice test: the
answers are given to you. ETS has actually given you the answers, and only
one of them is correct. The essence of this technique is to systematically Plug
In the Answers to see which answer choice works given the information in the
problem.
Strategy!
At the left is a tried-andtrue Princeton Review
strategy, PITA (which has
nothing to do with the
delicious type of bread).
Let’s look at an example of a Plugging In the Answers question.
An office supply store sells binder clips that cost 14 cents each and binder clips
that cost 16 cents each. If a customer purchases 85 binder clips from this store at a
total cost of $13.10, how many 14-cent binder clips does the customer purchase?
16
25
30
35
65
Are you tempted to try to
set up an algebraic equation? Are there no quickly
identifiable variables? Are
the answer choices real
numbers? Try Plugging In
the Answers!
Here’s How to Crack It
ETS would like you to solve this problem using algebra, and there is a good
chance that you started to think about the variables you could use to set up
some equations to solve this problem. That urge to do algebra is actually the
first sign that you can solve this problem using Plugging In the Answers.
Other signs that you can Plug In the Answers to solve this problem are that
the question asks for a specific amount and that the numbers in the answer
choices reflect that specific amount. With all these signs, it’s definitely time to
Plug In the Answers!
Start by setting up your scratch paper. To do so, just list the five answer
choices in a column, with the actual numbers included. Since the problem is
asking for the number of 14-cent binder clips purchased, these answer choices
have to represent the number of 14-cent binder clips purchased. Label this
column 14¢.
The answer choices will always be listed in either ascending or descending
numerical order, so when you Plug In the Answers, start with (C). By
determining whether or not (C) works, you can eliminate the other answer
choices that are either greater or less than (C), based on the result of this
answer choice. This effectively cuts the amount of work you need to do in
half. So, start with the idea that the customer purchased 30 binder clips that
cost 14 cents each. What can you figure out with this information? You’d
know that the total spent on these binder clips is 30 × $0.14 = $4.20. So, make
a column with the heading “amount spent” and write $4.20 next to (C). Now,
look for the next thing you’d know from this problem. If the customer
purchased a total of 85 binder clips and 30 of them cost 14 cents each, that
means that the customer purchased 55 16-cent binder clips. Make another
column with the heading “16¢” and write 55 in the row for (C). Next, make
another column for the amount spent on 16-cent binder clips, label it “amount
spent,” and write 55 × $0.16 = $8.80 under this column in the row for (C).
The next piece of information in the problem is that the customer spends a
total of $13.10 on the binder clips. This information allows you to determine
if (C) is correct. All Plugging In the Answers questions contain a condition
like this that lets you decide if the answer is correct. In this case, $4.20 +
$8.80 = $13.00, which is less than $13.10, so eliminate (C). Since the total
was not great enough, you can determine that to increase the total, the
customer must have purchased more 16-cent binder clips. Since (D) and (E)
would increase the number of 14-cent binder clips purchased, they cannot be
correct. Eliminate (D) and (E) as well.
Now, do the same steps starting with (B). If the customer purchased 25 of the
14-cent binder clips, they cost $3.50. The customer also purchased 60 of the
16-cent binder clips at a cost of $9.60. The total amount spent is $3.50 +
$9.60 = $13.10. Since this matches the amount spent in the problem, (B) is
correct.
Here’s what your scratch paper should look like after this problem:
When you want to Plug In the Answers, here are the steps that you should
follow.
Step 1:
Recognize the opportunity. There are three ways to do
this. The first indications are the phrases “how much…,”
“how many…,” or “what is the value of….” When you see
one of these phrases in a question, its a good indicator that
you may be able to Plug In the Answers. The second tipoff is specific numbers in the answer choices in ascending
or descending order. The last tip-off is your own
inclination. If you find yourself tempted to write your own
algebraic formulas and to invent your own variables to
solve the problem, it’s a good sign that you can Plug In the
Answer choices.
Step 2:
Set up the scratch paper. The minute you recognize the
opportunity, list the numbers in the answer choices in a
column on the scratch paper.
Step 3:
Label the first column. The question asks you to find a
specific number of something so the answer choices must
be options for that number. At the top of the column above
the answer choices, write down what the numbers
represent.
Step 4:
Start with (C). Choice (C) will always be the number in
the middle. This the most efficient place to start because it
will allow you to eliminate as many as three answer
choices if it is wrong.
Step 5:
Create your spreadsheet. Use (C) to work through the
problem. It is always easier to understand the problem
using a specific number. Work through the problem one
step at a time, and every time you have to do something
with the number, make a new column. Each column is a
step in solving the problem that you may need to use again
with a different answer choice, so don’t leave anything
out.
Step 6:
Repeat with the other answer choices. On single-answer
multiple-choice questions, only one answer choice can
work. If (C) is correct, you are finished with the problem.
If it is not correct, you may be able to determine if the
value of the number is too great or too small. If it is too
great, you can eliminate it and every answer choice that it
is greater than. The same thing can be done if the value of
the resulting answer is lesser than the value indicated by
the problem. At this point, you have basically created your
own little spreadsheet that is specfically designed to
calculate the correct answer. Check the remaining answer
choices by using the spreadsheet. As soon as you find an
answer choice that works, you’re finished.
On PITA questions, you don’t need to check all five answer choices because
only one of them can be correct. Once you have found an answer that works
with the problem, select it and move on to the next problem. PITA is a great
tool but it requires a high level of organization, so make sure to keep track of
everything that you do on the scratch paper.
PLUGGING IN ON QUANTITATIVE
COMPARISON QUESTIONS
Quantitative comparison, or quant comp, questions with variables can be
extremely tricky because the obvious answer is often wrong, whereas finding
the correct answer may involve a scenario that is not commonly thought of.
On the other hand, there is a simple set-up and approach that you can use to
help find the correct answers. As always, whenever you see variables, replace
them with real numbers. On quant comp questions, however, it is crucial that
you Plug In more than once and specifically that you plug in different kinds
of numbers that may not occur to you to think of initially. A good way to help
you think of this is to always keep the nature of the answer choices in mind.
Picking (A) means that you believe that the quantity in column A will always
be greater than Quantity B—no matter what number you plug in. Choice (B)
means that the quantity in column B will always be greater than Quantity A
—no matter what number you plug in, and so forth. To prove that one of these
statements is true you have to plug in every possible number that could
change the outcome. Don’t worry. We have a simple process to help figure out
what to plug in and how to track your progress as you do.
Quantitative comparison
questions often test your
knowledge of the
properties of fractions,
zero, one, negatives, and
other weird numbers.
Here are the steps:
Step 1:
Recognize the opportunity. The first seven or eight
questions of any Math section will be quant comp. When a
quant comp question appears and you see variables, you
know that you can Plug In.
Step 2:
Set up the scratch paper. The minute you see quant comp
and variables set up the scratch paper. The recommended
set up should look something like the diagram below.
Place Quantity A and B on either side. Quant comp
questions only have four potential answer choices, so write
(A), (B), (C), and (D) down as well, so you can eliminate
answers as you go. Finally, leave space to write down the
numbers that you plug in for the variables in between the
Quantities, so you can stay organized.
Step 3:
Plug In and eliminate. Start with an easy number, just
like outlined in the earlier Plugging In section, but make
sure that you also follow any conditions in the problem.
With the number you plugged in for the variable, solve for
Quantity A and Quantity B and write the solutions down.
If Quantity A is greater than Quantity B, eliminate (B) and
(C). If Quantity B is greater than Quantity A, eliminate (A)
and (C). If both quantities are the same, eliminate (A) and
(B).
Step 4:
Plug In again using FROZEN numbers. On quant comp
questions with variables, you always need to Plug In more
than once and the second time you do it, you need to use
FROZEN numbers. FROZEN is an acronym that will be
explained in the next section, as well the entire concept
behind why to Plug In more than once, so keep reading!
Always Plug In More Than Once on Quant
Comp Questions
Quant comp questions only have four options for answer choices but one of
those options, (D), can be selected if the relationship between Quantity A and
Quantity B cannot be determined based on the information given. After you
Plug In the first time, you need to Plug In again but this time you need to try
and choose a number that will produce a different outcome for the question.
While the first time you Plug In you can usually reliably eliminate two of
answer choices (A), (B), or (C), you Plug In again to try and make sure that
you can eliminate (D). Choice (D) can be eliminated only when you have a
high level of confidence that no matter what number you plug in, the answer
will always remain the same. If even one of the numbers you choose creates a
different answer, (D) should be selected.
On quant comp questions,
plug in easy numbers such
as 2 or 5, and eliminate
two choices. Then plug in
FROZEN numbers (Fractions, Repeats, One, Zero,
Extremes, Negatives)
to try to disprove your
first answer. If different
numbers give you different
answers, you’ve proved
that the answer is (D).
So, to eliminate (D) you need to choose a different number. But what makes a
number different and what makes for a good number to choose that might
create a different outcome for the problem? When you Plug In for the second
(or sometimes third or fourth) time in a quant comp question, you should pick
a FROZEN number. FROZEN is an acronym that highlights different types of
numbers and it stands for:
Fractions
Repeats
One
Zero
Extremes
Negatives
Fractions are numbers such as
or
that are great to use if the problem
contains exponents or roots, as fractions respond to these two stimuli in a
different way from whole numbers. Repeats are numbers that are found in the
question stem, can be used in both Quantities, or numbers that are implied by
the question stem (such as using the number 60 if the question is about
seconds, minutes, or hours). One and zero are special numbers because they
can result in two quantities being equal to each other, and each has a unique
effect on other numbers. Extreme numbers are numbers such as 10 or 100 that
should be used to see if the relationship between the quantities changes for
numbers that are greater than the one that was initially chosen. Negative
numbers, such as −2 or −3, are numbers that create different outcomes when
plugged in for variables, as they can make Quantities negative or positive,
which can alter the outcome.
FROZEN numbers can also be combined to create different numbers, such as
−100, − , or −1. Often ETS will create a quant comp question that has a
correct answer that depends on using these types of numbers. They do that
because they know that most people will not think of these numbers, which is
why it is important to Plug In more than once and, when you do, use
FROZEN numbers.
Let’s look at an example problem:
Quantity A
Quantity B
2x3
4x2
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
Step 1:
Recognize the opportunity. This is a quant comp
question and there are variables in the quantities, so this is
a Plug In problem.
Step 2:
Set up the scratch paper. Get yourself organized and
ready to answer the problem by setting up the scratch
paper.
Step 3:
Plug In. Let’s start with an easy number such as 2. Plug in
2 for x. When x = 2, the quantity in column A is 2 × 23 =
16, and the quantity in column B is 4 × 22 = 16 as well.
Since both quantities are equal in this case, neither
Quantity A nor Quantity B is always greater than the other,
so eliminate choices (A) and (B).
Step 4:
Plug In again using FROZEN numbers. Now look at the
problem and try to decide on a FROZEN number for x that
may create a different answer. Try One. If x = 1, then
Quantity A is 2 × 13 = 2 and Quantity B is 4 × 12 = 4.
Quantity B is now greater than Quantity A, which means
that (C) is incorrect. Eliminate (C) and select (D), which is
the correct answer.
If you chose to follow the recommended setup for the scratch paper, it should
look like this:
You might also have noticed that choosing different FROZEN numbers, such
as Fractions or Zero, would also yield a different result that would have
allowed you to eliminate (C). This is not uncommon as ETS is hoping you
forget to use these FROZEN numbers when Plugging In. Make sure you use
these numbers aggressively on quant comp problems because they can
radically affect the relationship between the two Quantities.
PLUGGING IN ON FRACTION AND PERCENT
PROBLEMS
Now that you’ve become familiar with fractions and percents, we’ll show you
a great method for solving many of these problems. When you come to
regular multiple-choice questions, or multiple-choice, multiple-answer
questions, that involve fractions or percents, you can simply plug in a number
and work through the problem using that number. This approach works even
when the problem doesn’t have variables in it. Why? Because, as you know,
fractions and percents express only a relationship between numbers—the
actual numbers don’t matter. For example, look at the following problem:
Plugging In on fraction
and percent problems is a
great way to make these
problems much easier.
A recent survey of registered voters in City X found that
of the respondents
support the mayor’s property tax plan. Of those who did not support the mayor’s
plan,
indicated they would not vote to reelect the mayor if the plan were
implemented. Of all the respondents, what fraction indicated that they would not
vote for the mayor if the plan were enacted?
What important information
is missing from the
problem?
Here’s How to Crack It
Even though there are no variables in this problem, we can still Plug In. On
fraction and percent problems, ETS will often leave out one key piece of
information: the total. Plugging In for that missing value will make your life
much easier. What crucial information did ETS leave out of this problem?
The total number of respondents. So let’s plug in a value for it. Let’s say that
there were 24 respondents to the survey. 24 is a good number to use because
we’ll have to work with
and
, so we want a number that’s divisible by
both those fractions. Working through the problem with our number, we see
that
of the respondents support the plan.
of 24 is 8, so that means 16
people do not support the plan. Next, the problem says that
not support the plan will not vote for the mayor.
of those who do
of 16 is 2, so 2 people
won’t vote for the mayor. Now we just have to answer the question: Of all
respondents, what fraction will not vote for the mayor? Well, there were 24
total respondents and we figured out that 2 aren’t voting. So that’s
, or
.
Choice (B) is the one we want.
ALGEBRA: OPERATIONS WITH VARIABLES
While Plugging In is a great strategy to make algebra problems easy on the
GRE by turning them into arithmetic, in many cases being comfortable
manipulating variables in an equation is necessary to answering a question.
Plugging In will help you solve for a variable in a question but sometimes the
question only requires you to manipulate an equation to get the correct
answer.
Dealing with Variables
The previous chapter familiarized you with number concepts and the previous
section showed you how to turn algebra into arithmetic by using Plugging In.
However, its time to learn the basics of dealing with variables and
manipulating equations to help make problems easier to work with and give
you the best opportunity to optimize your score.
Manipulating Equations
When working with equations, you can do pretty much anything you want to
them as long as you follow the golden rule:
Whatever you do on one side of the equals sign you must also do on the
other side.
Solving for One Variable
Let’s begin the discussion of manipulating equations with one variable by
solving for one variable. When presented with an equation with one variable,
start by isolating the variable on one side of the equation and the numbers on
the other side. You can do this by adding, subtracting, multiplying, or dividing
both sides of the equation by the same number. Just remember that anything
you do to one side of an equation, you must do to the other side. Let’s look at
a simple example:
3x − 4 = 5
Don’t assume you’ll
always need to solve
for the variable on the
GRE; sometimes you’ll
simply have to manipulate
the equation to get the
answer.
Here’s How to Crack It
When presented with a problem like this, your goal is to isolate the variable
on one side of the equation with all the real numbers, or constants, on the
other. In the example above, begin manipulating this question by adding 4 to
both sides of the equation. In general, you can eliminate negative numbers by
adding them to both sides of the equation, just as you can eliminate positives
by subtracting them from both sides of the equation.
The variable is not quite isolated yet, as it is still being multiplied by 3. In the
same way that you manipulated the equation earlier by moving the 4 to the
other side of the equation, you must move the 3. Since the 3 is being
multiplied to the variable, move it by doing the opposite operation, in this
case division. This allows you to solve for x and finish the problem.
x=3
Let’s try another one:
5x − 13 = 12 − 20x
Here’s How to Crack It
Again, we want to get all the x values on the same side of the equation. This
time, however, there is more than one instance of x so begin the question by
combining the x values.
As the problems get more
involved, make sure to
keep yourself organized by
utilizing the scratch paper
given to you.
Now that the values of x are combined, isolate the x by moving the negative
13 to the other side of the question.
Solve for x by finishing the isolation by moving the 25 that it is being
multiplied by.
25x = 25
x=1
Let’s try one more that is slightly more complicated.
5x +
= 7x
Here’s How to Crack It
The first thing you probably notice here is the fraction. Whenever you see an
equation like this that contains a fraction, begin by “clearing” the fraction. To
clear the fraction, multiply all the terms in the equation by the denominator of
the fraction. In this case, multiply all the terms by 2.
10x + 3 = 14x
You must always do the
same thing to both sides
of an equation.
Notice how all the terms have by multiplied by 2! This is very important, so
don’t forget to do it! Now, manipulate the equation to collect all the x’s on the
same side of the equation.
Now finish isolating the x by moving the 4.
3 = 4x
=x
WORKING WITH TWO VARIABLES
Many times, however, an equation on the GRE will involve two variables. An
example of an equation with two variables looks like this:
3x + 10y = 64
Here’s How to Crack It
The important thing to note about this situation is that we cannot solve this
equation. Why, you ask? The problem is that since there are two variables,
there are many possible solutions to this equation, all of which are equally
valid. For example, plugging in the values x = 8 and y = 4 would satisfy the
equation. But the equation would also be satisfied if you plugged in the values
x = 10 and y = 3.4. Therefore, the GRE cannot test an equation with two
variables without either providing a definitive way to solve for one of the
variables, or providing a second equation. By giving two equations, you are
able to find definitive values for the variables. So a more likely problem
would look something like this:
3x + 10y = 64
6x − 10y = 8
You can’t solve an
equation with two
variables unless you
have a second equation.
Now there are 2 variables and 2 equations, which means we can solve for the
variables. When two equations are given, look to combine them by adding or
subtracting the entire equations. We do this so that we can cancel out one of
the variables, leaving us with a simple equation with one variable. In this
case, it’s easier to add the two equations together, which will eliminate the y
variable as seen below.
Add these two equations to get 9x = 72. This is a simple equation, just like the
ones discussed in the previous section, which we can solve to find x = 8. Once
we’ve done that, we can solve for the other variable by inserting the value of
x into one of the original equations. For example, if we substitute x = 8 into
the first equation, we get 3(8) + 10y = 64, we can solve to find that y = 4.
The GRE will rarely give you two equations that line up as nicely as the
above example does, though. You are more likely to find two equations with
two variables and, while the variables match, the numbers associated with the
variables are not equal. In this case, you will need to manipulate one equation
so the numbers associated with a variable are equal. Doing this will allow the
elimination of a variable when the two equations are added or subtracted. Try
the next problem as an example.
4x + 7y = 41
2x + 3y = 19
Here’s How to Crack It
Notice here that the numbers associated with the variables are not equal,
which means that you cannot eliminate a variable. Adding the two equations
yields 6x + 10y = 60. That doesn’t help; it’s a single equation with two
variables, which is impossible to solve. Subtracting the equations leaves 2x +
4y = 22, which is also a single equation with two variables. To solve this
system of equations, we need to make the coefficient for one of the variables
in the first equation equal to the coefficient for that same variable in the
second equation. In this case, try multiplying the second equation by 2.
2(2x + 3y) = 2(19)
This gives us the following:
4x + 6y = 38
Now we can subtract this equation from the first equation. Doing this
operation yields y = 3. Now we can substitute y = 3 into either one of the
original equations to find that x = 5.
Simultaneous Equations
Thus far, we have learned how to manipulate equations with one variable and
two equations with two variables in order to solve for the variables. However,
it is not uncommon for ETS to give you two equations and ask you to use
them to find the value of a given expression. Much like manipulating two
equations with two variables, all you need to do is add or subtract the two
equations! The only difference is this time you won’t end up solving for an
individual variable.
Here’s an example:
If 5x + 4y = 6 and 4x + 3y = 5, then what does x + y equal?
Here’s How to Crack It
Remember that the problem is asking you to solve for x + y. This may appear
like you need to solve for the variables individually, but try to add or subtract
the equations first to see what they yield. First, try adding the two equations
together.
Since the problem wants the value of x + y and this gives us the value of 9x +
7y this is not useful. So try subtracting the two equations.
Bingo. The value of the expression (x + y) is exactly what we’re looking for.
You could have tried to solve for each variable individually and solved the
problem that way, but since the question is asking for the value of an
expression, it was easier to manipulate the equations like this. So remember,
on the GRE you may see two equations written horizontally. Now you know
that you don’t need complicated math to solve them! Just rewrite the two
equations, putting one on top of the other, and simply add or subtract them.
INEQUALITIES
The difference between an equation and an inequality is that in an equation
one side always equals the other and in an inequality one side does not equal
the other. Equations contain equal signs, while inequalities contain one of the
following symbols:
≠
>
<
≥
≤
is not equal to
is greater than
is less than
is greater than or equal to
is less than or equal to
The point of the inequality
sign always points to the
lesser value.
The good news is that inequalities are manipulated in the same way that you
manipulated any of the equations in the previous sections of this chapter.
However, there is one critical difference. When you multiply or divide both
sides of an inequality by a negative number, the direction of the inequality
symbol must change. So, if the inequality x > y is multiplied by −1, the
resulting inequality is –x < –y.
To see this rule in action, take a look at the following inequality:
12 − 6x > 0
Here’s How to Crack It
There are two ways to solve this inequality. You could manipulate this
inequality without ever multiplying or dividing by a negative number by just
adding 6x to both sides and then dividing both sides of the inequality by the
positive 6. In this case, the sign would not change, as seen below.
2>x
The other way to solve this inequality is to subtract 12 from both sides first.
This will create a situation where you need to divide both sides of the
equation by −6, as shown below.
x<2
Flip the sign! When you
multiply or divide both
sides of an inequality by
a negative number, the
greater than/less
than sign points the
opposite way.
Notice that the sign flipped because you divided both sides by a negative
number, but the answer for both methods of solving this inequality is the same
thing. The first answer says that the number 2 is greater than x, and the second
says that x is less than the number 2!
Inequalities show up on the GRE in a variety of ways. For instance, ETS may
give you a range for two variables and then ask you to combine them in some
way. This type of problem looks like the following question:
If 0 ≤ x ≤ 10 and −10 ≤ y ≤ −1, then what is the range for x – y?
Here’s How to Crack It
First, determine what the question is asking you to do. The question is asking
you to solve for the range for the expressions x – y. To determine this you
need to consider all possible combinations of x – y. Since the inequalities are
ranges themselves, find the greatest and least possible values of x – y by
calculating the largest x minus the largest y, the largest x minus the least y, the
least x minus the largest y, and the least x minus the least y. The greatest value
of x is 10 and the least value of x is 0. The greatest value of y is −1 and the
least value is −10. Calculate these values and keep yourself organized by
writing this all down on the scratch paper.
The calculations look as follows:
10 – (–1) = 11
10 – (–10) = 20
0 – (–1) = 1
0 – (–10) = 10
Since the least possible value of x – y is 0 – (–1) = 1 and the greatest possible
value of x – y is 10 – (–10) = 20, the range is 1 ≤ x – y ≤ 20.
QUADRATIC EQUATIONS
Quadratic equations are special types of equations that involve four terms.
Here is an example of a quadratic:
(x + 4)(x − 7)
In order to work with quadratics on the GRE, you must be familiar with two
concepts: FOIL and factoring.
Quadratic Equations
There are three quadratic equations that frequently appear on the
GRE. Knowing these equations both in their factored and unfactored
forms, can drastically improve your time on these questions. Here
they are:
1. Factored form: x2 – y2 (the difference between two squares)
Unfactored form: (x + y)(x – y)
2. Factored form: (x + y)2
Unfactored form: x2 + 2xy + y2
3. Factored form: (x – y)2
Unfactored form: x2 − 2xy + y2
FOIL
When you see a quadractic, you need to multiply every term in the first set of
parentheses by every term in the second set of parentheses. Use the acronym
FOIL to remember this method. FOIL stands for first, outer, inner, last. For
example, if you see (x + 4) (x + 3), you would multiply the first terms (x × x),
the outer terms (x × 3), the inner terms (4 × x), and the last terms (4 × 3), as
follows:
(x × x) + (x × 3) + (4 × x) + (4 × 3) =
x2 + 3x + 4x + 12 =
x2 + 7x + 12
We know to use plus signs inside the parentheses because both the 7 and the
12 are positive. Now we have to think of two numbers that, when added
together, give us 7, and when multiplied together, give us 12.
Find these numbers by listing the factor pairs of 12. Those pairs are 1 and 12,
2 and 6, and 3 and 4. The only pair that equals 7 when they are added together
is 4 and 3, so insert those into the equation.
(x + 4) (x + 3) = 0
To find the solutions, set each factor equal to 0 and solve. So, x + 4 = 0 and x
+ 3 = 0. So x can either be −4 or −3.
Let’s look at a question that uses quadratics that you may see on the GRE.
Quantity A
(4 +
) (4 –
Quantity B
)
10
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
First, eliminate (D) because there are only numbers in this question, so the
answer can be determined. Now, Quantity A looks like a job for FOIL!
Multiply the first terms, and you get 16. Multiply the outer terms and you get
−4 . Multiply the inner terms to get 4 . Multiply the last terms to get −6.
So, Quantity A is now 16 −4
+4
− 6. The two inner terms cancel each
other out and all the remains is 16 − 6, or 10. Since Quantity B is also equal to
10, the two answer choices are equal and the correct answer is (C). You might
also notice that Quantity A is one of the common quadratics: (x + y)(x − y) =
x2 − y2. Therefore, (4 +
)(4 −
) = 42 −( )2 = 16 − 6 = 10.
Factoring
The process of factoring “undoes” the FOIL process. Factoring is commonly
tested on the GRE so you should be very familiar with the process. Think of
factoring as taking a quadratic in the opposite direction of FOIL. Here is a
quadratic in its unfactored, or expanded, form:
x2 − 10x + 24
We are going to factor this quadratic using the following steps:
1. Separate the x2 into (x ) (x ).
2. Find the factors of the third term that, in this case the number 24,
when added or subtracted, yield the second term, the number 10.
Note here that we are not concerned with the variable x.
3. Figure out the signs (+/–) for the terms. The signs have to yield the
middle number when added and the last term when multiplied.
If we apply these steps to the quadratic given earlier, we begin the problem by
splitting x2 into
(x ) (x )
Next, write down the factors of the third term, 24. The factors are 1 and 24, 2
and 12, 3 and 8, and 4 and 6. Of these pairs of factors, which contains two
numbers that we can add or subtract to get the second term, 10? 4 and 6 is the
only pair that works, so put those into the parentheses.
(x 4)(x 6)
The final step is to figure out the signs. We need to end up with a negative 10
and a positive 24. If we add −6 and −4, we’ll get −10. Similarly, if we
multiply −6 and −4, we’ll end up with 24. So the factored form of the
quadratic is
(x − 4)(x − 6)
Solving Quadratic Equations
ETS likes to use quadratic equations because they have an interesting quirk;
when you solve a quadratic equation, you usually get two possible answers as
opposed to one. For this reason, quadratic equations are perfect ways for ETS
to try to trick you.
Here’s an example:
x2 + 2x − 15 = 0
Quantity A
Quantity B
2
x
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Quadratic equations
usually have two solutions.
Here’s How to Crack It
In order to solve a quadratic equation, the equation must be set equal to zero.
Normally, this will already be the case on the GRE, as it is in this example.
But if you encounter a quadratic equation that isn’t set equal to zero, you must
first manipulate the equation so that it is. Next you must factor the equation;
otherwise you cannot solve it. So let’s factor the quadratic equation in this
example. We need to figure out the factors of 15 that we can add or subtract to
give us 2. The only possible factors are 3 and 5. In order to get a negative 15
and a positive 2, we need to use 5 and −3. So that leaves us
(x − 3)(x + 5) = 0
Next, we’re going to solve each of the two factors within parentheses
separately:
x − 3 = 0 and x + 5 = 0
Thus, x = 3 and x = −5. If x = 3, then Quantity B is greater, but if x = −5 then
Quantity A is greater. This means that the correct answer is (D).
Let’s try another one:
If x2 + 8x + 16 = 0, then what is the value of x ?
Here’s How to Crack It
Let’s factor the equation. Start with (x ) (x ). Next, find the factors of 16
that add or subtract to 8. The factors of 16 are 1 and 16, 2 and 8, and 4 and 4.
Of these pairs, only 4 and 4 have a sum of 8. Since we have a positive 8 and a
positive 16, the signs for both numbers must be positive. Thus, we end up
with (x + 4) (x + 4) = 0. Now, we need to solve the equation. If x + 4 = 0, then
x = −4. This is the number we’d enter into the text box on the GRE.
Let’s look at one more example.
If x and y are positive integers, and if x2 + 2xy + y2 = 25, then what is the value of
(x + y)3 ?
5
15
50
75
125
Here’s How to Crack It
While this problem may look like a lot of work, if you have committed the
common quadratic equations from earlier in this section to memory the
answer is easier to come by. The equation in this question is reflective of the
common quadratic: x2 + 2xy + y2 = (x + y)2. The question tells us that x2 + 2xy
+ y2 is equal to 25, which means that (x + y)2 is also equal to 25. Think of x +
y as one unit that, when squared, is equal to 25. Since this question specifies
that x and y are positive integers, what positive integer squared equals 25?
The number 5 does, so x + y = 5. The question is asking for (x + y)3. In other
words, what’s 5 cubed, or 5 × 5 × 5? The answer is (E), 125.
EXPONENTS AND SQUARE ROOTS
Finally, the last section of this chapter is going to deal with exponents and
square roots. Questions with exponents and square roots are common on the
GRE and solving these questions often requires manipulating the exponents
or roots. Here’s the information you need to know in order to work with them.
What Are Exponents?
Exponents are a sort of mathematical shorthand for repeated multiplication.
Instead of writing (2)(2)(2)(2), you can use an exponent and write 24. The
little 4 is the power and the 2 is called the base. The power tells you how
many times to multiply the base by itself. Knowing this terminology will be
helpful in following the discussion in this section.
The Five Rules of Working with Exponents
For the GRE there are five major rules that apply when you work with
exponents. The more comfortable you are with these rules, the more likely
you will be to approach an exponent question with confidence and get the
answer correct!
The first three rules deal with the combination and manipulation of
exponents. Those three rules are represented by the acronym MADSPM,
which stands for:
Multiply
Add
Divide
Subtract
Power
Multiply
These three rules will be explained in more detail shortly, but for now just
remember:
•
when you see exponents with equal bases which are being
multiplied, you add the powers;
•
when equal bases are divided you subtract the exponents; and
•
when an exponent is raised to a power, you multiply the powers.
The fourth rule is the definition of a negative exponent. The fifth and final
rule is the definition of a zero exponent.
The Multiply-Add Rule of Exponents
When two exponents with equal bases are multiplied, you must add the
exponents. Consider the following example:
32 × 33
As defined earlier, a power just tells you how many times to multiply a base
by itself. So another way to write this expression is:
32 × 33 = (3 × 3)(3 × 3 × 3) = 35
As you can see, the number of bases, which in this case is the integer 3, that
are actually being multiplied together is five, as there are two 3’s that are
represented by 32 and three 3’s that are represented by 33.
Now solve this question more quickly by using the multiply-add rule.
32 × 33 = 32+3 = 35
The Divide-Subtract Rule of Exponents
When two exponents with equal bases are divided, you must subtract the
exponents. Consider the following example and expand the exponents to
make it clear.
=5
Now, instead of expanding the exponents just apply the divide-subtract rule
for the same problem.
= 53−2 = 51 = 5
The Power-Multiply Rule of Exponents
When an expression with an exponent is raised to another power, multiply the
powers together. Consider the following example and expand the exponents to
make it clear.
(62)3 = (62) (62) (62) = (6 × 6) (6 × 6) (6 × 6) = 66
Now, apply the power-multiply rule to solve the same problem.
(62)3 = 62×3 = 66
For all of these rules, the bases must be the same. So, for example, you could
not divide-subtract the expression
because the bases are not the same.
Negative Exponents
A negative exponent is another way ETS uses exponents on the GRE.
Consider the following example.
So when you have a negative exponent, all that needs to be done is to put the
entire expression in a fraction, with 1 in the numerator and the exponent in the
denominator, and change the negative exponent to a positive. A term raised to
a negative power is the reciprocal of that term raised to the positive power.
Zero Exponents
Sometimes ETS will give you an exponent question that, after you have
successfully manipulated it, results in a base number raised to a power of 0.
Any nonzero number raised to a power of 0 is equal to 1. Consider the
following example.
43 × 4–3 = 43–3 = 40 = 1
Exponent Tips Beyond the Five Rules
Sometimes you will have an exponent problem for which none of the five
rules discussed apply. If you reach this point there are two tips to keep you
moving forward.
Tip 1: Rewrite Terms Using Common Bases
ETS will always write questions that work out nicely, so if none of the bases
in an exponent question seem to match up, see if you can find a way to
rewrite the bases so that they match, and you will be able to use one of the
five rules.
Tip 2: Look for a Way to Factor the Expression
Factoring the expression is often a way to reveal something about the
exponent expression that you may not have noticed before. If you get stuck
with an exponent question try to factor the expression and see if there is a way
to use one of the five rules.
It will be uncommon for ETS to just test one or two of these concepts on a
GRE problem. Most times, two or more of these concepts will be combined to
create a problem. Let’s look at a couple of examples.
If y ≠ 0, which of the following is equivalent to
?
y
y2
y3
y4
y5
Here’s How to Crack It
Begin by simplifying the denominator of the fraction. Use the power-multiply
rule to combine (y2)3 into y6. Since a number, or in this case a variable, by
itself is the same thing as having that number or variable raised to a power of
1, use the add-multiply rule to combine y(y6) into y7. Now use the dividesubtract rule to solve the problem; the correct answer is (B).
Let’s look at another problem.
Quantity A
Quantity B
1515 − 1514
1514(14) − 1
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
The question wants you to compare the two quantities but since none of the
rules for exponents apply here, see if there is something else you can do to
this problem. The expression in Quantity A can be factored so begin there.
Quantity A is now 1515 − 1514 = 1514(15 − 1), which is the same thing as
1514(14). Notice how this is the same as Quantity B, except Quantity B is 1
less than 1514(14). Therefore, Quantity A is greater and the correct answer is
(A).
Take a look at one more exponent problem.
If x ≠ 0 and 643 = 8x then what is the value of x2 ?
5
6
25
36
64
Here’s How to Crack It
Solve this question by determining the value for x. To solve for x in this
equation, start by rewriting the exponent expressions using a common base.
Since 64 can be written as 82, the equation can be rewritten as (82)3 = 8x.
Since the bases are the same, for the equation to be equal the powers have to
be the same as well. (82)3 can be rewritten as 86 because of the powermultiply rule, so if 86 = 8x then x = 6. Now plug that number into the value for
x2. This is now 62 which equals 36, so the correct answer is (D).
The Peculiar Behavior of Exponents
•
Raising a number greater than 1 to a power greater than 1 results
in a greater number. For example, 22 = 4.
•
Raising a fraction that’s between 0 and 1 to a power greater than 1
results in a lesser number. For example,
.
•
A negative number raised to an even power results in a positive
number. For example, (–2)2 = 4, because (–2)(–2) = 4.
•
A negative number raised to an odd power results in a negative
number. For example, (–2)3 = −8, because (–2)(–2)(–2) = −8.
•
A number raised to the first power ALWAYS results in the number
itself. For example, 1,0001 = 1,000.
What Is a Square Root?
The radical sign
indicates the square root of a number. For example,
means that some number times itself is equal to 4. In this case, since 22 = 4 it
can be determined that
= 2. Think of square roots as the opposite of
exponents. If you want to eliminate a square root in an equation, all you need
to do is raise that square root to a power of 2. Just remember to do that for all
of the elements in the equation!
Square roots can only exist on the GRE with nonnegative numbers. If the
problem states that x2 = 16, then x = ±4 as both a positive and a negative 4,
when multiplied by itself, yields 16. However, when you find the square root
of any number, the result will always be positive.
Rules for Square Roots
There are rules that dictate what you can and cannot do with square roots, just
like there are rules about exponents.
You can multiply and
divide any square roots,
but you can add or
subtract roots only when
the number under the
radical sign is the same.
Adding and Subtracting Square Roots
You can only add or subtract square roots if the values under the radical sign
are equal. So, for example, the expression can be simplified to because the
value under the radical sign is equal. Conversely, the expression cannot be
reduced any further because the values of the roots are not the same.
Rules for Adding and Subtracting Square Roots
a
+b
= (a + b)
a
−b
= (a − b)
Multiplying and Dividing Square Roots
Any square roots can be multiplied or divided. There aren’t any restrictions
on this so keep an eye out for opportunities to combine roots by multiplying
or dividing that could make a root easier to work with. For example,
= 6. Roots can be divided as well; for example,
=
= 2.
Rules for Multiplying and Dividing Square Roots
Simplifying Square Roots
Often times when you multiply square roots on the GRE, you will not get
numbers under the radical sign that work out perfectly. When this happens,
you will need to simplify the square root. You simplify a square root by
looking for ways to factor the number under the root that results in a least one
perfect square. A perfect square is an integer that when the square root of that
integer is taken, the result is another integer. For example, 4 is a perfect
square because
= 2. Similarly, 9 and 25 are perfect squares because
=
3 and
= 5, respectively. Look at the following expression and try to
simplify it.
You can combine this expression to result in
. However, this is not in the
most simplified form. Look for ways to factor 20 in which one of the pairs of
numbers is a perfect square. The factors of 20 are 1 and 20, 2 and 10, and 4
and 5. Since 4 is a perfect square, this can now be simplified even further.
Now let’s take a look at some examples of how ETS might test roots on the
GRE.
What is the value of the expression 3
−2
?
4
5
10
12
20
Here’s How to Crack It
The problem is subtracting roots. Since roots cannot be subtracted unless the
numbers under the radical sign are equal, look for a way to simplify the roots.
Since 5 cannot be simplified any further, work with 80. The factors of 80 are
1 and 80, 2 and 40, 4 and 20, 5 and 16, and 8 and 10. Two of these pairs of
factors contain a perfect square, but one contains a perfect square and a prime
number. This is a good thing. This means that it could be reduced no further,
so choose 5 and 16 and simplify to read 3
=3
= (3 × 4 ) = 12
. Now that the bases are equal, subtract the expression to find that 12
−
2
= 10 , which is (C). The same answer would have been found if the
numbers 4 and 20 had been chosen as the factors of 80, but there would have
been another round of simplifying the root, as 20 would have needed to be
reduced to 4 and 5 as factors.
Here’s another problem.
z2 = 144
Quantity A
Quantity B
z
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
The trap answer here is (C). Remember that if z2 = 144, then the value of z is
either 12 or −12. However, when a value is under a radical sign—that is,
when you’re looking for the square root—it can only be positive. Therefore,
Quantity A could be 12 or −12 and Quantity B can only be 12. Since there is
no way to ensure that one is always greater than the other, the correct answer
is (D).
Try one more problem:
What is the value of
?
3
3
3
To Simplify Roots:
1. Rewrite the number as
the product of two
factors, one of which is
a perfect square.
2. Use the multiplication
rule for roots.
Here’s How to Crack It
First, simplify each of these roots.
has a factor that is a perfect square—
25, so it can be rewritten as
and simplified to 5
perfect square 9 as a factor, so it can be written as
to 3
. This means that
is equal to
; the
.
has the
and then simplified
in the numerator and
denominator cancel, leaving . The correct answer is (A).
Algebra (And When to Use It) Drill
Now it’s time to try out what you have learned on some practice questions.
Try the following problems and then check your answers in Part V.
1 of 10
The original selling price of an item at a store is 40 percent more than the cost of the item to the retailer.
If the retailer reduces the price of the item by 15 percent of the original selling price, then the difference
between the reduced price and the cost of the item to the retailer is what percent of the cost of the item
to the retailer?
2 of 10
x2 + 8x = −7
Quantity A
Quantity B
x
0
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
3 of 10
If 33 × 912 = 3x, what is the value of x ?
4 of 10
If A = 2x – (y − 2c) and B = (2x – y) − 2c, then A – B =
–2y
–4c
–0
–2y
–4c
5 of 10
A merchant sells three different sizes of canned tomatoes. A large can costs the same as 5 medium cans
or 7 small cans. If a customer purchases an equal number of small and large cans of tomatoes for the
same amount of money needed to buy 200 medium cans, how many small cans does she purchase?
35
45
72
199
208
6 of 10
If 6k − 5l = 27 and 3l − 2k = −13 and 5k − 5l = j, what is the value of j ?
7 of 10
If a is multiplied by 3 and the result is 4 less than 6 times b, what is the value of a − 2b ?
−12
−
−
12
8 of 10
Quantity A
Quantity B
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
9 of 10
11x + 14y = 30 and 3x + 4y = 12
Quantity A
Quantity B
x+y
(x + y)−2
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
10 of 10
If x = 3a and y = 9b, then all of the following are equal to 2(x + y) EXCEPT
3(2a + 6b)
6(a + 3b)
24( a + b)
(18a + 54b)
12( a + b)
Summary
Plugging In converts algebra problems to arithmetic problems. Plug In
by replacing variables in the question with real numbers or by working
backwards from the answer choices provided.
Use easy numbers first when Plugging In for variables. If the need
arises to Plug In again, use the FROZEN numbers to help eliminate
tricky answer choices on math problems.
The golden rule of equations: Whatever you do to one side of the
equation, you must do to the other. This applies to all equations,
whether they are equal or not.
In order to solve an equation with two variables, you need two
equations. Stack them up and add or subtract to cancel out one of the
variables.
Inequalities are manipulated the same way that other equations are,
with one notable difference: Always remember to flip the sign when
you multiply or divide by a negative number.
Use the FOIL process to expand quadratics. To solve a quadratic
equation, set it equal to zero, and factor.
An exponent is shorthand for repeated multiplication. When in doubt on
exponent problems, look to find common bases or ways to factor the
expressions.
Think of a square root as the opposite of an exponent. Square roots are
always positive.
Chapter 12
Real World Math
Real world math is our title for the grab bag of math topics that will be
heavily tested on the GRE. This chapter details a number of important math
concepts, many of which you’ve probably used at one point or another in your
daily adventures, even if you didn’t recognize them. After completing this
chapter, you’ll have brushed up on important topics such as ratios,
proportions, and averages. You’ll also learn some important Princeton Review
methods for organizing your work and efficiently and accurately answering
questions on these topics.
EVERYDAY MATH
A few years ago when ETS reconfigured the GRE, they wanted the Math
section to test more of what they call “real life” scenarios that a typical
graduate student might see. You can therefore expect the math questions on
the GRE to heavily test topics such as proportions, averages, and ratios—
mathematical concepts that are theoretically part of your everyday life.
Regardless of whether that’s true of your daily life or not, you’ll have to
master these concepts in order to do well on the GRE Math section.
The math on the GRE
is supposed to reflect
the math you use in your
day-to-day activities.
RATIOS AND PROPORTIONS
If you’re comfortable working with fractions and percentages, you’ll be
comfortable working with ratios and proportions, because ratios and
proportions are simply special types of fractions. Don’t let them make you
nervous. Let’s look at ratios first and then we’ll deal with proportions.
What Is a Ratio?
Recall that a fraction expresses the relationship of a part to the whole. A ratio
expresses a different relationship: part to part. Imagine yourself at a party
with 8 women and 10 men in attendance. Remembering that a fraction
expresses a part-to-whole relationship, what fraction of the partygoers are
female?
, or 8 women out of a total of 18 people at the party. But what’s the
ratio, which expresses a part to part relationship, of women to men?
, or as
ratios are more commonly expressed, 8 : 10. You can reduce this ratio to 4 : 5,
just like you would a fraction.
A ratio is just another type
of fraction.
On the GRE, you may see ratios expressed in several different ways:
x:y
the ratio of x to y
x is to y
In each case, the ratio is telling us the relationship between parts of a whole.
Every Fraction Can Be a Ratio, and Vice Versa
Every ratio can be expressed as a fraction. A ratio of 1 : 2 means that the total
of all the parts is either 3 or a multiple of 3. So, the ratio 1 : 2 can be
expressed as the fraction
fractions of the whole as
, or the parts of the ratio can be expressed as
and . Likewise, the fraction
expresses the ratio
1 : 3. So if a question says “the ratio of x to 2y is ,” then that would be
expressed as
= .
Treat a Ratio Like a Fraction
Anything you can do to a fraction you can also do to a ratio. You can crossmultiply, find common denominators, reduce, and so on.
Find the Total
The key to dealing with ratio questions is to find the whole, or the total.
Remember: A ratio tells us only about the parts, not the total. In order to find
the total, add the numbers in the ratio. A ratio of 2 : 1 means that there are
three total parts. A ratio of 2 : 5 means that we’re talking about a total of 7
parts. And a ratio of 2 : 5 : 7 means there are 14 total parts. Once you have a
total you can start to do some fun things with ratios.
For example, let’s say you have a handful of pennies and nickels. If you have
30 total coins and the pennies and nickels are in a 2 : 1 ratio, how many
pennies do you have? The total for our ratio is 3, meaning that out of every 3
coins, there are 2 pennies and 1 nickel. So if there are 30 total coins, there
must be 20 pennies and 10 nickels. Notice that
is the same as , is the
same as 2 : 1!
Like a fraction, a ratio
expresses a relationship
between numbers.
When you are working with ratios, there’s an easy way not only to keep track
of the numbers in the problem but also to quickly figure out the values in the
problem. It’s called the Ratio Box. Let’s try the same question, but with some
different numbers; if you have 24 coins in your pocket and the ratio of
pennies to nickels is 2 : 1, how many pennies and nickels are there? The Ratio
Box for this question is below, with all of the information we’re given already
filled in.
The minute you see the
word “ratio,” draw a Ratio
Box on your scratch paper.
Remember that ratios are relationships between numbers, not actual numbers,
so the real total is 24; that is, you have 24 actual coins in your pocket. The
ratio total (the number you get when you add the number of parts in the ratio)
is 3.
The middle row of the table is for the multiplier. How do you get from 3 to
24? You multiply by 8. Remember when we talked about finding equivalent
fractions? All we did was multiply the numerator and denominator by the
same value. That’s exactly what we’re going to do with ratios. This is what
the Ratio Box looks like now:
The multiplier is the key
concept in working with
ratios. Just remember that
whatever you multiply one
part by, you must multiply
every part by.
Now let’s finish filling in the box by multiplying everything else.
Therefore, of the 24 coins 16 are pennies and 8 are nickels.
Let’s try a GRE example.
Flour, eggs, yeast, and salt are mixed by weight in the ratio of 11 : 9 : 3 : 2,
respectively. How many pounds of yeast are there in 20 pounds of the mixture?
1
1
2
2
8
Here’s How to Crack It
The minute you see the word ratio, draw a Ratio Box on your scratch paper
and fill in what you know.
First, add all of the numbers in the ratio to get the ratio total.
Now, what do we multiply 25 by to get 20?
25x = 20
x=
x=
So
is our “multiply by” number. Let’s fill it in.
The question asks for the amount of yeast, so we don’t have to worry about
the other ingredients. Just look at the yeast column. All we have to do is
multiply 3 by
and we have our answer: 3 ×
=
= 2 , which is (D).
What Is a Proportion?
So you know that a fraction is a relationship between part and whole, and that
a ratio is a relationship between part and part. A proportion is an equivalent
relationship between two fractions or ratios. Thus,
because they are equivalent fractions. But
and
and
are proportionate
are not in proportion
because they are not equal ratios.
The GRE often contains problems in which you are given two proportional, or
equal, ratios from which one piece of information is missing. These questions
take a relationship or ratio, and project it onto a larger or smaller scale.
Proportion problems are recognizable because they always give you three
values and ask for a fourth value. Here’s an example:
The key to proportions is
setting them up correctly.
If the cost of a one-hour telephone call is $7.20, what would be the cost in dollars
of a 10-minute telephone call at the same rate?
Here’s How to Crack It
It’s very important to set up proportion problems correctly. That means
placing your information on your scratch paper. Be especially careful to label
everything. It takes only an extra two or three seconds, but doing this will
help you catch lots of errors.
For this question, let’s express the ratios as dollars over minutes, because
we’re being asked to find the cost of a 10-minute call. That means that we
have to convert 1 hour to 60 minutes (otherwise it wouldn’t be a proportion).
Now cross-multiply.
60x = (7.20)(10)
60x = 72
x=
Now we can enter 1.20 into the box.
Relationship Review
You may have noticed a trend in the preceding pages. Each of the
major topics covered—fractions, percents, ratios, and proportions—
described a particular relationship between numbers. Let’s review:
•
A fraction expresses the relationship between a part and
the whole.
•
A percent is a special type of fraction, one that expresses
the relationship of part to whole as a fraction with the
number 100 in the denominator.
•
A ratio expresses the relationship between part and part.
Adding the parts of a ratio gives you the whole.
•
A proportion expresses the relationship between equal
fractions, percents, or ratios.
•
Each of these relationships shares all the characteristics of
a fraction. You can reduce them, expand them, multiply
them, and divide them using the exact same rules you used
for working with fractions.
AVERAGES
The average (arithmetic mean) of a list of numbers is the sum, or total value,
of all the numbers in the list divided by the number of numbers in the list. The
average of the list 1, 2, 3, 4, 5 is equal to the total of the numbers (1 + 2 + 3 +
4 + 5, or 15) divided by the number of numbers in the list (which is 5).
Dividing 15 by 5 gives us 3, so 3 is the average of the list.
GRE average problems
always give you two of
the three numbers needed.
ETS always refers to an average as an “average (arithmetic mean).” This
confusing parenthetical remark is meant to keep you from being confused by
other more obscure kinds of averages, such as geometric and harmonic
means. You’ll be less confused if you simply ignore the parenthetical remark
and know that average means total of the elements divided by the number of
elements.
Think Total
Don’t try to solve average problems all at once. Do them piece by piece. The
key formula to keep in mind when doing problems that involve averages is
Average =
Drawing an Average Pie will help you organize your information.
The minute you see the
word average, draw
an Average Pie on your
scratch paper.
Here’s how the Average Pie works. The total is the sum of the numbers being
averaged. The number of things is the number of different elements that you
are averaging. And the average is, naturally, the average.
Say you wanted to find the average of 4, 7, and 13. You would add those
numbers to get the total and divide that total by three.
4 + 7 + 13 = 24
=8
Mathematically, the Average Pie works like this:
Which two pieces of the
pie do you have?
The horizontal bar is a division bar. If you divide the total by the number of
things, you get the average. If you divide the total by the average, you get the
number of things. If you have the number of things and the average, you can
simply multiply them together to find the total. This is one of the most
important things you need to be able to do to solve GRE average problems.
Using the Average Pie has several benefits. First, it’s an easy way to organize
information. Furthermore, the Average Pie makes it clear that if you have two
of the three pieces, you can always find the third. This makes it easier to
figure out how to approach the problem. If you fill in the number of things,
for example, and the question wants to know the average, the Average Pie
shows you that the key to unlocking that problem is finding the total.
Try this one.
The average (arithmetic mean) of seven numbers is 9 and the average of three of
these numbers is 5. What is the average of the other four numbers?
4
5
7
10
12
Draw a new Average Pie
each time you encounter
the word average in a
question.
Here’s How to Crack It
Let’s take the first sentence. You have the word average, so draw an Average
Pie and fill in what you know. We have seven numbers with an average of 9,
so plug those values into the Average Pie and multiply to find the total.
Now we also know that three of the numbers have an average of 5, so draw
another Average Pie, plug those values into their places, and multiply to find
the total of those three numbers.
The question is asking for the average of the four remaining numbers. Draw
one more Average Pie and plug in 4 for the number of things.
In order to solve for the average, we need to know the total of those four
numbers. How do we find this? From our first Average Pie we know that the
total of all seven numbers is 63. The second Average Pie tells us that the total
of three of those numbers was 15. Thus, the total of the remaining four has to
be 63 − 15, which is 48. Plug 48 into the last Average Pie, and divide by 4 to
get the average of the four numbers.
The average is 12, which is (E).
Let’s try one more.
The average (arithmetic mean) of a set of 6 numbers is 28. If a certain number, y, is
removed from the set, the average of the remaining numbers in the set is 24.
Quantity A
Quantity B
y
48
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
All right, let’s attack this one. The problem says that the average of a set of
six numbers is 28, so let’s immediately draw an Average Pie and calculate the
total.
If a certain number, y, is removed from the set, there are now five numbers
left. We already know that the new average is 24, so draw another Average
Pie.
The difference between the totals must be equal to y. 168 − 120 = 48. Thus,
the two quantities are equal, and the answer is (C).
Up and Down
Averages are very predictable. You should make sure you automatically know
what happens to them in certain situations. For example, suppose you take
three tests and earn an average score of 90. Now you take a fourth test. What
do you know?
If your average goes up as a result of the fourth score, then you know that
your fourth score was higher than 90. If your average stays the same as a
result of the fourth score, then you know that your fourth score was exactly
90. If your average goes down as a result of the fourth score, then you know
that your fourth score was less than 90.
MEDIAN, MODE, AND RANGE
The median is the middle value in a list of numbers; above and below the
median lie an equal number of values. For example, in the list of numbers (1,
2, 3, 4, 5, 6, 7) the median is 4, because it’s the middle number (and there are
an odd number of numbers in the list). If the list contained an even number of
integers such as (1, 2, 3, 4, 5, 6) the median is the average of 3 and 4, or 3.5.
When looking for the median, sometimes you have to put the numbers in
order yourself. What is the median of the list of numbers (13, 5, 6, 3, 19, 14,
8)? First, put the numbers in order from least to greatest, (3, 5, 6, 8, 13, 14,
19). Then take the middle number. The median is 8. Just think median =
middle and always make sure the numbers are in order.
Don’t confuse
median and mode!
The mode is the number in a list of numbers that occurs most frequently. For
example, in the list (2, 3, 4, 5, 3, 8, 6, 9, 3, 9, 3) the mode is 3, because 3
shows up the most. Just think mode = most.
When you see the word
median in a question, put
the numbers in the
problem in order.
The range is the difference between the greatest and the least numbers in a
list of numbers. So, in the list of numbers (2, 6, 13, 3, 15, 4, 9), the range is 15
(the greatest number in the list) − 2 (the least number in the list), or 13.
Here’s an example:
Set F = {4, 2, 7, 11, 8, 9}
What do we need to do to
the numbers in this set?
Quantity A
Quantity B
The range of Set F
The median of Set F
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
Let’s put the numbers in order first, so it’ll be easier to see what we have: {2,
4, 7, 8, 9, 11}. First, let’s look at Quantity A: The range is the greatest
number, or 11, minus the least number, or 2. That’s 9. Now let’s look at
Quantity B: The minute you see the word median, be sure to put the numbers
in order. The median is the middle number of the set, but because there are
two middle numbers, 7 and 8, we have to find the average. Or do we? Isn’t
the average of 7 and 8 clearly going to be smaller than the number in Quantity
A, which is 9? Yes, in quant comp questions, we compare, not calculate. The
answer is (A).
STANDARD DEVIATION
Standard deviation is one of those phrases that math people like to throw
around to scare non-math people, but it’s really not that scary. The GRE might
ask you questions about standard deviation, but you’ll never have to actually
calculate it; instead, you’ll just need a basic understanding of what standard
deviation is. In order to understand standard deviation, we must first look at
something all standardized testers should be familiar with, the bell curve.
You’ll never have to calculate
the standard deviation
on the GRE.
Your Friend the Bell Curve
The first thing to know about a bell curve is that the number in the middle is
the mean.
Imagine that 100 students take a test and the results follow a normal
distribution. When you see the phrase normal distribution, draw a bell curve.
Let’s say that the average score on this test is an 80. Put 80 in the middle of
the curve. You also know that 2% of the students got a 96 or higher. Put a 96
above the right 2% line on the curve.
Standard deviation measures how much a score differs from the norm (the
average) in even increments. The curve tells us that a score earned by only
2% of the students is two standard deviations from the norm. If the norm is 80
and 96 is two standard deviations away, then one standard deviation on this
test is 8 points. Why? Remember that standard deviations are even
increments. If the average is 80 and the score two standard deviations from
the norm is 96, then the difference is 16. So, one standard deviation is half of
that difference, or 8. The score at one standard deviation greater than the
norm is, therefore, 88. Two standard deviations above the norm is 96, while
two standard deviations below the norm is 64. One standard deviation below
the norm is 72. Fill these in on your bell curve.
Now you know quite a bit about the distribution of scores on this test: 68% of
the students received a score between 72 and 88, and 98% percent scored
above a 64. That’s all there is to know about standard deviations. The
percentages don’t change, so memorize those. When you see the phrase, just
draw a bell curve and fill in what you know. Here’s what the curve looks like
for this test:
Here’s an example of how ETS might test standard deviation:
Quantity A
Quantity B
The standard deviation of a list
of data consisting of 10
integers ranging from −20 to
−5
The standard deviation of a list
of data consisting of 10
integers ranging from 5 to 20
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
ETS is hoping you’ll make a couple of wrong turns on this problem. The first
trap they set is that one list of numbers contains negative integers while the
other doesn’t—but this doesn’t mean that one list has a negative standard
deviation. Standard deviation is defined as the distance a point is from the
mean, so it can never be negative. The second trap is that ETS hopes you’ll
waste a lot of time trying to calculate standard deviation based on the
information given. But you know better than to try to do that. Remember that
ETS won’t ask you to calculate standard deviation; it’s a complex calculation.
Plus, as you know, you need to know the mean in order to calculate the
standard deviation and there’s no way we can find it based on the information
here. Thus, we have no way of comparing these two quantities, and the
answer is (D).
Now let’s try a question that will make use of the bell curve.
The fourth grade at School X is made up of 300 students who have a total weight of
21,600 pounds. If the weight of these fourth-graders has a normal distribution and
the standard deviation equals 12 pounds, approximately what percentage of the
fourth-graders weigh more than 84 pounds?
12%
16%
36%
48%
60%
Here’s How to Crack It
This one’s a little tougher than the earlier standard deviation questions. The
first step is to determine the average weight of the students, which is = 72
pounds. If the standard deviation is 12 pounds, then 84 pounds places us
exactly one standard deviation above the mean, or at the 50 + 34 = 84th
percentile (remember the bell curve?). Because 16 percent of all students
weigh more than 84 pounds, the answer is (B).
RATE
Rate problems are similar to average problems. A rate problem might ask for
an average speed, distance, or the length of a trip, or how long a trip (or a job)
takes. To solve rate problems, use the Rate Pie.
A rate problem is really
just an average problem.
The Rate Pie works exactly the same way as the Average Pie. If you divide
the distance or amount by the rate, you get the time. If you divide the distance
or amount by the time, you get the rate. If you multiply the rate by the time,
you get the distance or amount.
Let’s take a look.
It takes Carla three hours to drive to her brother’s house at an average speed of 50
miles per hour. If she takes the same route home, but her average speed is 60 miles
per hour, what is the time, in hours, that it takes her to drive home?
2 hours
2 hours and 14 minutes
2 hours and 30 minutes
2 hours and 45 minutes
3 hours
Here’s How to Crack It
The trip to her brother’s house takes three hours, and the rate is 50 miles per
hour. Plug those numbers into a Rate Pie and multiply to find the distance.
So the distance is 150 miles. On her trip home, Carla travels at a rate of 60
miles per hour. Draw another Rate Pie and plug in 150 and 60. Then all you
have to do is divide 150 by 60 to find the time.
So it takes Carla two and a half hours to get home. That’s (C).
Try another one.
A machine can stamp 20 envelopes in 4 minutes. How many of these machines,
working simultaneously, are needed to stamp 60 envelopes per minute?
5
10
12
20
24
Here’s How to Crack It
First we have to find the rate per minute of one machine. Plug 20 and 4 into a
Rate Pie and divide to find the rate.
The rate is 5. If one machine can stamp 5 envelopes per minute, how many
machines do you need to stamp 60 per minute? 60 ÷ 5 = 12, or (C).
CHARTS
Every GRE Math section has a few questions that are based on a chart or
graph (or on a group of charts or graphs). But don’t worry; the most important
thing that chart questions test is your ability to remember the difference
between real-life charts and ETS charts.
In real life, charts are often provided in order to display information in a way
that’s easier to understand. Conversely, ETS constructs charts to hide
information you need to know and to make that information harder to
understand.
Chart questions frequently
test percents, percent
change, ratios, proportions, and averages.
Chart Questions
There are usually two or three questions per chart or per set of charts. Like the
Reading Comprehension questions, chart questions appear on split screens.
Be sure to click on the scroll bar and scroll down as far as you can; there may
be additional charts underneath the top one, and you want to make sure
you’ve seen all of them.
On charts, look for the
information ETS is trying
to hide.
Chart problems just recycle the basic arithmetic concepts we’ve already
covered: fractions, percentages, and so on. This means you can use the
techniques we’ve discussed for each type of question, but there are two
additional techniques that are especially important to use when doing chart
questions.
Don’t Start with the Questions: Start with the Charts
Take a minute to note the following key bits of information from any
chart you see.
•
Information in titles: Make sure you know what each chart
is telling you.
•
Asterisks, footnotes, parentheses, and small print: Often
there will be crucial information hidden away at the bottom
of the chart. Don’t miss it!
•
Funny units: Pay special attention when a title says “in
thousands” or “in millions.” You can usually ignore the units
as you do the calculations, but you have to use them to get
the right answer.
Using Your Smarts
on Charts
Pay attention to small
details like footnotes,
parentheses, tiny print,
and even odd units.
These usually provide key
insights that will enrich
your understanding of the
chart.
Approximate, Estimate, and Ballpark
Like some of our other techniques, you have to train yourself to estimate
when working with charts and graphs questions. You should estimate, not
calculate exactly, in the following situations:
•
whenever you see the word approximately in a question
•
whenever the answer choices are far apart in value
•
whenever you start to answer a question and you justifiably say to
yourself, “This is going to take a lot of calculation!”
Don’t try to work
with huge values.
Ballpark instead!
Review those “friendly” percentages and their fractions from earlier in the
chapter. Try estimating this question:
What is approximately 9.6 percent of 21.4 ?
Here’s How to Crack It
Use 10 percent as a friendlier percentage and 20 as a friendlier number. Onetenth of 20 is 2 (it says “approximately”—who are you to argue?). That’s all
you need to do to answer most chart questions.
Chart Problems
Make sure you’ve read everything on the chart carefully before you try the
first question.
Approximately how many tons of aluminum and copper combined were purchased
in 1995 ?
125
255
325
375
515
How much did Company X spend on aluminum in 1990 ?
$675,000
$385,000
$333,000
$165,000
$139,000
Approximately what was the percent increase in the price of aluminum from 1985
to 1995 ?
8%
16%
23%
30%
42%
Here’s How to Crack the First Question
As you can see from the graph on the previous page, in 1995, the black bar
(which indicates aluminum) is at 250, and the dark gray bar (which indicates
copper) is at approximately 125. Add those figures and you get the number of
tons of aluminum and copper combined that were purchased in 1995: 250 +
125 = 375. That’s (D). Notice that the question says “approximately.” Also
notice that the numbers in the answer choices are pretty far apart.
Here’s How to Crack the Second Question
We need to use the chart and the graph to answer this question, because we
need to find the number of tons of aluminum purchased in 1990 and multiply
it by the price per ton of aluminum in 1990 in order to figure out how much
was spent on aluminum in 1990. The bar graph tells us that 175 tons of
aluminum was purchased in 1990, and the little chart tells us that aluminum
was $2,200 per ton in 1990. 175 × $2,200 = $385,000. That’s (B).
Here’s How to Crack the Third Question
Remember that percent increase formula from earlier in this chapter?
Percent change =
or
× 100
We’ll need to use the little chart for this one. In 1985, the price of aluminum
was $1,900 per ton. In 1995, the price of aluminum was $2,700 per ton. Now
let’s use the formula. 2,700 − 1,900 = 800, so that’s the difference. This is a
percent increase problem, so the original number is the smaller one. Thus, the
original is 1,900, and our formula looks like this: Percent change =
100. By canceling the 0’s in the fraction you get
gives you
×
× 100, and multiplying
. At this point you could divide 800 by 19 to get the exact
answer, but because they’re looking for an approximation, let’s round 19 to
20. What’s 800 ÷ 20? That’s 40, and (E) is the only one that’s close.
Need More Math
Review?
Check out Math Workout
for the GRE. If you’re in
a hurry, pick up Crash
Course for the GRE.
Real World Math Drill
Now it’s time to try out what you have learned on some practice questions.
Try the following problems and then check your answers in Part V.
1 of 12
Sadie sells half the paintings in her collection, gives one-third of her paintings to friends, and keeps the
remaining paintings for herself. What fraction of her collection does Sadie keep?
2 of 12
5x − 2y = 2y − 3x
Quantity A
Quantity B
x
y
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Questions 3 through 5 refer to the following graph.
3 of 12
If the six New England states are ranked by population in Year X and Year Y, how many states would
have a different ranking from Year X to Year Y ?
None
One
Two
Three
Four
4 of 12
In Year X, the population of Massachusetts was approximately what percent of the population of
Vermont?
50%
120%
300%
800%
1,200%
5 of 12
By approximately how much did the population of Rhode Island increase from Year X to Year Y ?
750,000
1,250,000
1,500,000
2,250,000
3,375,000
6 of 12
A water jug with a capacity of 20 gallons is 20 percent full. At the end of every third day, water is added
to the jug. If the amount of water added is equal to 50 percent of the water in the jug at the beginning of
that day, how many days does it take for the jug to be at least 85% full?
4
6
12
15
20
7 of 12
Towns A, B, C, and D are all in the same voting district. Towns A and B have 3,000 people each who
support referendum R and the referendum has an average (arithmetic mean) of 3,500 supporters in
towns B and D and an average of 5,000 supporters in Towns A and C.
Quantity A
Quantity B
The average number of
supporters of Referendum R in
Towns C and D
The average number of
supporters of Referendum R in
Towns B and C
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
8 of 12
A company paid $500,000 in merit raises to employees whose performances were rated A, B, or C. Each
employee rated A received twice the amount of the raise that was paid to each employee rated C; and
each employee rated B received one-and-a-half times the amount of the raise that was paid to each
employee rated C. If 50 workers were rated A, 100 were rated B, and 150 were rated C, how much was
the raise paid to each employee rated A ?
$370
$625
$740
$1,250
$2,500
Questions 9 through 11 refer to the following graphs.
9 of 12
In 2013, the median reading test score for ninth-grade students was in which score range?
Below 65 points
65–69 points
70–79 points
80–89 points
90–100 points
10 of 12
If the number of students in grades 9 through 12 comprised 35 percent of the number of students in
School District X in 1995, then approximately how many students were in School District X in 1995 ?
9,700
8,700
3,400
3,000
1,200
11 of 12
Assume that all students in School District X took the reading test each year. In 2013, approximately
how many more ninth-grade students had reading test scores in the 70–79 point range than in the 80–89
point range?
470
300
240
170
130
12 of 12
One ounce of Solution X contains only ingredients a and b in a ratio of 2 : 3. One ounce of Solution Y
contains only ingredients a and b in a ratio of 1 : 2. If Solution Z is created by mixing solutions X and Y
in a ratio of 3 : 11, then 630 ounces of Solution Z contains how many ounces of a ?
68
73
89
219
236
Summary
A ratio expresses a part to part relationship. The key to ratio problems
is finding the total. Use the ratio box to organize ratio questions.
A proportion expresses the relationship between equal fractions,
percents, or ratios. A proportion problem always provides you with
three pieces of information and asks you for a fourth.
Use the Average Pie to organize and crack average problems.
The median is the middle number in a set of values. The mode is the
value that appears most frequently in a set. The range of a set is the
difference between the largest and smallest values in the set.
You will never have to calculate standard deviation on the GRE.
Standard deviation problems are really average and percent problems.
Make sure you know the percentages associated with the bell curve:
34%, 14%, 2%.
Use the Rate Pie for rate questions.
On chart questions, make sure you take a moment to understand what
information the chart is providing. Estimate answers to chart questions
whenever possible.
Chapter 13
Geometry
Chances are you probably haven’t used the Pythagorean theorem recently or
had to find the area of a circle in quite a while. However, you’ll be expected
to know geometry concepts such as these on the GRE. This chapter reviews
all the important rules and formulas you’ll need to crack the geometry
problems on the GRE. It also provides examples of how such concepts will be
tested on the GRE Math section.
WHY GEOMETRY?
Good question. If you’re going to graduate school for political science or
linguistics or history or practically anything that doesn’t involve math, you
might be wondering why the heck you have to know the area of a circle or the
Pythagorean theorem for this exam. While we may not be able to give you a
satisfactory answer to that question, we can help you do well on the geometry
questions on the GRE.
Expect to see a handful
of basic geometry
problems on each of
your Math sections.
WHAT YOU NEED TO KNOW
The good news is that you don’t need to know much about actual geometry to
do well on the GRE; we’ve boiled down geometry to the handful of bits and
pieces that ETS actually tests.
Before we begin, consider yourself warned: Since you’ll be taking your test
on a computer screen, you’ll have to be sure to transcribe all the figures onto
your scrap paper accurately. All it takes is one mistaken angle or line and
you’re sure to get the problem wrong. So make ample use of your scratch
paper and always double-check your figures. Start practicing now, by using
scratch paper with this book.
Another important thing to know is that you cannot necessarily trust the
diagrams ETS gives you. Sometimes they are very deceptive and are intended
to confuse you. Always go by what you read, not what you see.
DEGREES, LINES, AND ANGLES
For the GRE, you will need to know that
1. A line is a 180-degree angle. In other words, a line is a perfectly
flat angle.
2. When two lines intersect, four angles are formed; the sum of these
angles is 360 degrees.
3. When two lines are perpendicular to each other, their intersection
forms four 90-degree angles. Here is the symbol ETS uses to
indicate perpendicular lines: ⊥ .
4. Ninety-degree angles are also called right angles. A right angle on
the GRE is identified by a little box at the intersection of the
angle’s arms.
5. The three angles inside a triangle add up to 180 degrees.
6. The four angles inside any four-sided figure add up to 360 degrees.
7. A circle contains 360 degrees.
8. Any line that extends from the center of a circle to the edge of the
circle is called a radius (plural is radii).
Vertical Angles
Vertical angles are the angles that are across from each other when two lines
intersect. Vertical angles are always equal. In the drawing below, angle x is
equal to angle y (they are vertical angles) and angle a is equal to angle b (they
are also vertical angles).
On the GRE, the measure
of only one of the vertical
angles is typically shown.
But usually you’ll need
to use the other angle to
solve the problem.
Parallel Lines
Parallel lines are lines that never intersect. When a pair of parallel lines is
intersected by a third, two types of angles are formed: big angles and small
angles. Any big angle is equal to any big angle, and any small angle is equal
to any small angle. The sum of any big angle and any small angle will always
equal 180. When ETS tells you that two lines are parallel, this is what is being
tested. The symbol for parallel lines and the word parallel are both clues that
tell you what to look for in the problem. The minute you see either of them,
immediately identify your big and small angles; they will probably come into
play.
l1 and l2 are parallel
Quantity A
Quantity B
a+b
180
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
Notice that you’re told that these lines are parallel. Here’s one very important
point: You need to be told that. You can’t assume that they are parallel just
because they look like they are.
Okay, so as you just learned, only two angles are formed when two parallel
lines are intersected by a third line: a big angle (greater than 90 degrees) and a
small one (smaller than 90 degrees). More importantly, you learned that all
the big angles are equal, and all the small angles are equal. Therefore, the
angle directly across l1 from angle a is the same as angle b. These now form a
straight line, so a + b = 180, and the correct answer is (C).
TRIANGLES
Triangles are perhaps ETS’s favorite geometrical shape. Triangles have many
properties, which make them great candidates for standardized test questions.
Make sure you familiarize yourself with the following triangle facts.
Triangles are frequently
tested on the GRE.
The Rule of 180°
Every triangle contains three angles that add up to 180 degrees. You must
know this fact cold for the exam. This rule applies to every triangle, no matter
what it looks like. Here are some examples:
Equilateral Triangles
An equilateral triangle is a triangle in which all three sides are equal in
length. Because all of the sides are equal in these triangles, all of the angles
are equal. Each angle is 60 degrees because 180 divided by 3 is 60.
Isosceles Triangles
An isosceles triangle is a triangle in which two of the three sides are equal in
length. This means that two of the angles are also equal.
Angle/Side Relationships in Triangles
In any triangle, the longest side is opposite the largest interior angle; the
shortest side is opposite the smallest interior angle. That’s why the
hypotenuse of a right triangle is its longest side—there couldn’t be another
angle in the triangle bigger than 90 degrees. Furthermore, equal sides are
opposite equal angles.
Perimeter of a Triangle
The perimeter of a triangle is simply a measure of the distance around it. All
you have to do to find the perimeter of a triangle is add up the lengths of the
sides.
The Third Side Rule
Why is it impossible for the following triangle to exist?
This triangle could not exist because the length of any one side of a triangle is
limited by the lengths of the other two sides. This can be summarized by the
third side rule:
The length of any one side of a triangle must be less than the sum of the
other two sides and greater than the difference between the other two
sides.
This rule is not tested frequently on the GRE, but when it is, it’s usually the
key to solving the problem. Here’s what the rule means in application: Take
the lengths of any two sides of a triangle. Add them together, then subtract
one from the other. The length of the third side must lie between those two
numbers.
Take the sides 3 and 5 from the triangle above. What’s the longest the third
side could measure? Just add and subtract. It could not be as long as 8 (5 + 3)
and it could not be as short as 2 (5 − 3).
Therefore, the third side must lie between 2 and 8. It’s important to remember
that the third side cannot be equal to either 2 or 8. It must be greater than 2
and less than 8.
Try the following question:
A triangle has sides 4, 7, and x. Which of the following could be the perimeter of
the triangle?
Indicate all such perimeters.
13
16
17
20
22
Here’s How to Crack It
Remember the third side rule of triangles here, which is how to find possible
lengths of the third side of a triangle when given the two other sides. The
third side rule dictates that the length of the third side of a triangle must be
greater than the difference, but less than the sum, of the length of the two
known sides. In this particular problem, the two known sides are 4 and 7. The
difference between 4 and 7 is 3, and the sum of 4 and 7 is 11, so the third side
of the triangle must be greater than 3 and less than 11. This can be represented
by the expression 3 < x < 11. Use these values to create a range for the
possible perimeter of the triangle. If the third side of the triangle is 3, and the
other two sides are 4 and 7, the perimeter is 3 + 4 + 7 = 14. If the third side of
the triangle is 11, and the other two sides are 4 and 7, then the perimeter is 11
+ 4 + 7 = 22. Because the third side of the triangle is greater than 3 and less
than 11, the perimeter of the triangle must be greater than 14 and less than 22.
This can be represented by the expression 14 < perimeter < 22. The only
answer choices that fall in that range are (B), (C), and (D), which are the
correct answers.
Area of a Triangle
The area of any triangle is equal to its height (or altitude) multiplied by its
base, divided by 2, so
A = bh
Any time you see the
word area or any other
word that indicates that
a formula is to be used,
write the formula on your
scratch paper and park the
information you’re given
directly underneath.
The height of a triangle is defined as the length of a perpendicular line drawn
from the point of the triangle to its base.
The height of a triangle
must be perpendicular to
the base.
This area formula works on any triangle.
The Pythagorean Theorem
The Pythagorean theorem applies only to right triangles. This theorem states
that in a right triangle, the square of the length of the hypotenuse (the longest
side, remember?) is equal to the sum of the squares of the lengths of the two
other sides. In other words, c2 = a2 + b2, where c is the length of the
hypotenuse and a and b are the lengths of the other sides. (The two sides that
are not the hypotenuse are called the legs.)
ETS will sometimes try to
intimidate you by using
multiples of the common
Pythagorean triples. For
example, you might see a
10-24-26 triangle. That’s
just a 5-12-13 in disguise.
You can always use the Pythagorean theorem to calculate the third side of a
right triangle.
Here are the most common right triangles:
Note that a triangle could have sides with actual lengths of 3, 4, and 5, or 3 : 4
: 5 could just be the ratio of the sides. If you double the ratio, you get a
triangle with sides equal to 6, 8, and 10. If you triple it, you get a triangle with
sides equal to 9, 12, and 15.
Let’s try an example.
In the figure above, if the distance from point P to point Q is 6 miles and the
distance from point Q to point R is 10 miles, what is the distance from point P to
point R ?
4
5
6
7
8
Write everything down on
scratch paper! Don’t do
anything in your head.
Here’s How to Crack It
Once you’ve sensitized yourself to the standard right triangles, this problem
couldn’t be easier. When you see a right triangle, be suspicious. One leg is 6.
The hypotenuse is 10. The triangle has a ratio of 3 : 4 : 5. Therefore, the third
side (the other leg) must be 8.
The Pythagorean theorem will sometimes help you solve problems that
involve squares or rectangles. For example, every rectangle or square can be
divided into two right triangles. This means that if you know the length and
width of any rectangle or square, you also know the length of the diagonal—
it’s the shared hypotenuse of the hidden right triangles.
Here’s an example:
In the rectangle above, what is the area of triangle ABD ?
Here’s How to Crack It
We were told that this is a rectangle (remember that you can never assume!),
which means that triangle ABD is a right triangle. Not only that, but it’s a 3 : 4
: 5 right triangle (with a side of 3 and a hypotenuse of 5, it must be), with side
AD = 4. So, the area of triangle ABD is
That’s
the base (3) times the height (4).
of 12, or 6. Enter that value into the box.
Right Isosceles Triangles
If you take a square and cut it in half along its diagonal, you will create a right
isosceles triangle. The two sides of the square stay the same. The 90-degree
angle will stay the same, and the other two angles that were 90 degrees each
get cut in half and are now 45 degrees. The ratio of sides in a right isosceles
triangle is x : x : x
. This is significant for two reasons. First, if you see a
problem with a right triangle and there is a
anywhere in the problem, you
know what to look for. Second, you always know the length of the diagonal of
a square because it is one side times the square root of two.
You always know the
length of the diagonal
of a square because it is
one side of the square
times
Let’s try an example involving a special right triangle.
.
In the figure above, what is the area of square ABDE ?
28
49
49
98
98
Here’s How to Crack It
In order to figure out the area of square ABDE, we need to know the length of
one of its sides. We can get the length of BD by using the isosceles right
triangle attached to it. BD is the hypotenuse, which means its length is 7
.
To get the area of the square we have to square the length of the side we
know, or (7
)(7
) = (49)(2) = 98. That’s (D).
30 : 60 : 90 Triangles
If you take an equilateral triangle and draw in the height, you end up cutting it
in half and creating a right triangle. The hypotenuse of the right triangle has
not changed; it’s just one side of the equilateral triangle. One of the 60-degree
angles stays the same as well. The angle where the height meets the base is 90
degrees, naturally, and the side that was the base of the equilateral triangle has
been cut in half. The smallest angle, at the top, opposite the smallest side, is
30 degrees. The ratio of sides on a 30 : 60 : 90 triangle is x : x
what it looks like:
: 2x. Here’s
You can always calculate
the area of an equilateral
triangle because you know
that the height is one half
of one side times
.
This is significant for two reasons. The first is that if you see a problem with a
right triangle and one side is double the other or there is a
anywhere in the
problem, you know what to look for. The second is that you always know the
area of an equilateral triangle because you always know the height. The
height is one half of one side times the square root of 3.
Here’s one more:
Triangle XYZ in the figure above is an equilateral triangle. If the perimeter of the
triangle is 12, what is its area?
2
4
8
12
8
If you see
or
in
the answer choices of the
problem, it’s a tip-off that
the problem is testing
special right triangles.
Here’s How to Crack It
Here we have an equilateral triangle with a perimeter of 12, which means that
each side has a length of 4 and each angle is 60 degrees. Remember that in
order to find the area of a triangle, we use the triangle area formula: A =
bh,
but first we need to know the base and the height of the triangle. The base is
4, which now gives us A =
4h, and now the only thing we need is the height.
Remember: The height always has to be perpendicular to the base. Draw a
vertical line that splits the equilateral triangle in half. The top angle is also
split in half, so now we have this:
What we’ve done is create two 30 : 60 : 90 right triangles, and we’re going to
use one of these right triangles to find the height. Let’s use the one on the
right. We know that the hypotenuse in a 30 : 60 : 90 right triangle is always
twice the length of the short side. Here we have a hypotenuse (YZ) of 4, so
our short side has to be 2. The long side of a 30 : 60 : 90 right triangle is
always equal to the short side multiplied by the square root of 3. So if our
short side is 2, then our long side must be 2
. That’s the height.
Finally, we return to our area formula. Now we have A =
Multiply it out and you get A = 4
× 4 × 2
.
. The answer is (B).
FOUR-SIDED FIGURES
The four angles inside any figure that has four sides add up to 360 degrees.
That includes rectangles, squares, and parallelograms. Parallelograms are
four-sided figures made out of two sets of parallel lines whose area can be
found with the formula A = bh, where h is the height of a line drawn
perpendicular to the base.
Perimeter of a Rectangle
The perimeter of a rectangle is just the sum of the lengths of its four sides.
perimeter = 4 + 8 + 4 + 8
Area of a Rectangle
The area of a rectangle is equal to its length times its width. For example, the
area of the rectangle above is 32 (or 8 × 4).
Squares
A square has four equal sides. The perimeter of a square is, therefore, four
times the length of any side. The area of a square is equal to the length of any
side times itself, or in other words, the length of any side, squared. The
diagonal of a square splits it into two 45 : 45 : 90, or isosceles, right triangles.
CIRCLES
Circles are a popular test topic for ETS. There are a few properties that the
GRE likes to test over and over again and problems with circles also always
seem to use that funny little symbol π. Here’s all you need to know about
circles.
The World of Pi
You may remember being taught that the value of pi (π) is 3.14, or
even 3.14159. On the GRE, π = 3ish is a close enough approximation.
You don’t need to be any more precise than that when doing GRE
problems.
What you might not recall about pi is that pi (π) is the ratio between
the circumference of a circle and its diameter. When we say that π is a
little bigger than 3, we’re saying that every circle is about three times
as far around as it is across.
Chord, Radius, and Diameter
A chord is a line that connects two points on the circumference of a circle.
The radius of a circle is any line that extends from the center of the circle to a
point on the circumference of the circle. The diameter of a circle is a line that
connects two points on the circumference of the circle and that goes through
the center of the circle. Therefore, the diameter of a circle is twice as long as
its radius. Notice as well that the diameter of a circle is also the longest chord
and that a radius is not a chord.
The radius is always the
key to circle problems.
Circumference of a Circle
The circumference of a circle is like the perimeter of a triangle: It’s the
distance around the outside. The formula for finding the circumference of a
circle is 2 times π times the radius, or π times the diameter.
circumference = 2πr or πd
Circumference is
just a fancy way of
saying perimeter.
If the diameter of a circle is 4, then its circumference is 4π, or roughly 12+. If
the diameter of a circle is 10, then its circumference is 10π, or a little more
than 30.
An arc is a section of the outside, or circumference, of a circle. An angle
formed by two radii is called a central angle (it comes out to the edge from
the center of the circle). There are 360 degrees in a circle, so if there is an arc
formed by, say, a 60-degree central angle, and 60 is
of 360, then the arc
formed by this 60-degree central angle will be
of the circumference of the
circle.
Area of a Circle
The area of a circle is equal to π times the square of its radius.
area = πr2
When working with π,
leave it as π in your calculations.
Also, leave
as
. The answer will have
them that way.
Let’s try an example of a circle question.
In the wheel above, with center O, the area of the entire wheel is 169π. If the area
of the shaded hubcap is 144π, then t =
Here’s How to Crack It
We have to figure out what t is, and it’s going to be the length of the radius of
the entire wheel minus the length of the radius of the hubcap. If the area of the
entire wheel is 169π, the radius is
144π, the radius is
, or 13. If the area of the hubcap is
, or 12. 13 − 12 = 1. Enter this value into the box.
Let’s try another one.
In the figure above, a circle with the center O is inscribed in square WXYZ. If the
circle has radius 3, then PZ =
6
3
6+
3+
3
+3
Ballparking answers will
help you eliminate choices.
Here’s How to Crack It
Inscribed means that the edges of the shapes are touching. The radius of the
circle is 3, which means that PO is 3. If Z were at the other end of the
diameter from P, this problem would be easy and the answer would be 6,
right? But Z is beyond the edge of the circle, which means that PZ is a little
more than 6. Let’s stop there for a minute and glance at the answer choices.
We can eliminate anything that’s “out of the ballpark”—in other words, any
answer choice that’s less than 6, equal to 6 itself, or a lot more than 6.
Remember when we told you to memorize a few of those square roots?
Let’s use them:
(A) Exactly 6? Nope.
(B) That’s 1.4 × 3, which is 4.2. Too small.
(C) That’s 6 + 1.4, or 7.4. Not bad. Let’s leave that one in.
(D) That’s 3 + 1.7, or 4.7. Too small.
(E) That’s (3 × 1.4) + 3, which is 4.2 + 3, or 7.2. Not bad.
Let’s leave that one in too.
So we eliminated three choices with Ballparking. We’re left with (C) and (E).
You could take a guess here if you had to, but let’s do a little more geometry
to find the correct answer.
Because this circle is inscribed in the square, the diameter of the circle is the
same as a side of the square. We already know that the diameter of the circle
is 6, so that means that ZY, and indeed all the sides of the square, are also 6.
Now, if ZY is 6, and XY is 6, what’s XZ, the diagonal of the square? Well, XZ
is also the hypotenuse of the isosceles right triangle XYZ. The hypotenuse of a
right triangle with two sides of 6 is 6
. That’s approximately 6 × 1.4, or 8.4.
The question is asking for PZ, which is a little less than XZ. It’s somewhere
between 6 and 8.4. The pieces that aren’t part of the diameter of the circle are
equal to 8.4 − 6, or 2.4. Divide that in half to get 1.2, which is the distance
from the edge of the circle to Z. That means that PZ is 6 + 1.2, or 7.2. Check
your remaining answers: Choice (C) is 7.4, and (E) is 7.2. Bingo! The answer
is (E).
THE COORDINATE SYSTEM
On a coordinate system, the horizontal line is called the x-axis and the
vertical line is called the y-axis. The four areas formed by the intersection of
these axes are called quadrants. The point where the axes intersect is called
the origin. This is what it looks like:
To express any point in the coordinate system, you first give the horizontal
value, then the vertical value, or (x, y). In the diagram above, point A can be
described by the coordinates (2, 4). That is, the point is two spaces to the right
of the origin and four spaces above the origin. Point B can be described by the
coordinates (–6, 1). That is, it is six spaces to the left and one space above the
origin. What are the coordinates of point C? Right, it’s (−5, −5).
Coordinate geometry
questions often test basic
shapes such as triangles
and squares.
Here’s a GRE example:
Points (x, 5) and (–6, y), not shown in the figure above, are in Quadrants I and III,
respectively. If xy ≠ 0, in which quadrant is point (x, y) ?
IV
III
II
I
It cannot be determined from the information given.
Here’s How to Crack It
If point (x, 5) is in Quadrant I, that means x is positive. If point y is in
Quadrant III, then y is negative. The quadrant that would contain coordinate
points with a positive x and a negative y is Quadrant IV. That’s (A).
Slope
Trickier questions involving the coordinate system might give you the
equation for a line on the grid, which will involve something called the slope
of the line. The equation of a line is
y = mx + b
In this equation x and y are both points on the line, b stands for the yintercept, or the point at which the line crosses the y-axis, and m is the slope
of the line. Slope is defined as the vertical change divided by the horizontal
change, often called “the rise over the run” or the “change in y over the
change in x.”
Slope =
Sometimes on the GRE, m is written instead as a, as in y = ax + b. You’ll see
all this in action in a moment.
The line y = − x + 1 is graphed on the rectangular coordinate axes.
Quantity A
uantity B
OR
OP
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
The y-intercept, or b, in this case is 1. That means the line crosses the y-axis at
1. So the coordinates of point P are (0, 1). Now we have to figure out what
the coordinates of point R are. We know the y-coordinate is 0, so let’s stick
that into the equation (the slope and the y-intercept are constant; they don’t
change).
y = mx + b
0=− x+1
Now let’s solve for x.
0=− x+1
0−1=− x+1−1
−1=− x
=x
So the coordinates of point R are ( , 0). That means OR, in Quantity A, is
equal to , and OP, in Quantity B, is equal to 1. The answer is (B).
Another approach to this question would be to focus on the meaning of slope.
Because the slope is − , that means the vertical change is 8 and the horizontal
change is 7. In other words, you count up 8 and over 7. Clearly the rise is
more than the run; thus OP is more than OR.
Incidentally, if you’re curious about the difference between a positive and
negative slope, any line that rises from left to right has a positive slope. Any
line that falls from left to right has a negative slope. (A horizontal line has a
slope of 0, and a vertical line is said to have “no slope.”)
VOLUME
You can find the volume of a three-dimensional figure by multiplying the area
of a two-dimensional figure by its height (or depth). For example, to find the
volume of a rectangular solid, you would take the area of a rectangle and
multiply it by the depth. The formula is lwh (length × width × height). To find
the volume of a circular cylinder, take the area of a circle and multiply by the
height. The formula is πr2 times the height (or πr2h).
DIAGONALS IN THREE DIMENSIONS
There’s a special formula that you can use if you are ever asked to find the
length of a diagonal (the longest distance between any two corners) inside a
threedimensional rectangular box. It is a2 + b2 + c2 = d2, where a, b, and c are the
dimensions of the figure (kind of looks like the Pythagorean theorem, huh?).
Questions that ask about
diagonals are really about
the Pythagorean theorem.
Take a look:
What is the length of the longest distance between any two corners in a rectangular
box with dimensions 3 inches by 4 inches by 5 inches?
5
12
5
12
50
Here’s How to Crack It
Let’s use our formula, a2 + b2 + c2 = d2. The dimensions of the box are 3, 4,
and 5.
That’s (C).
SURFACE AREA
The surface area of a rectangular box is equal to the sum of the areas of all of
its sides. In other words, if you had a box whose dimensions were 2 × 3 × 4,
there would be two sides that are 2 by 3 (this surface would have an area of
6), two sides that are 3 by 4 (area of 12), and two sides that are 2 by 4 (area of
8). So, the total surface area would be 6 + 6 + 12 + 12 + 8 + 8, which is 52.
Don’t confuse surface
area with volume.
Key Formulas and Rules
Here is a review of the key rules and formulas to know for the GRE
Math section.
Lines and angles
•
All straight lines have 180 degrees.
•
A right angle measures 90 degrees.
•
Vertical angles are equal.
•
Parallel lines cut by a third line have two kinds of angles:
big angles and small angles. All of the big angles are equal
and all of the small angles are equal. The sum of a big
angle and a small angle is 180 degrees.
Triangles
•
All triangles have 180 degrees.
•
The angles and sides of a triangle are in proportion—the
largest angle is opposite the largest side and the smallest
side is opposite the smallest angle.
•
The Pythagorean theorem is c2 = a2 + b2 where c is the
length of the hypotenuse.
•
The area formula for a triangle is A =
.
Quadrilaterals
•
All quadrilaterals have 360 degrees.
•
The area formula for a squares and rectangles is bh.
Circles
•
All circles have 360 degrees.
•
The radius is the distance from the center of the circle to
any point on the edge.
•
The area of a circle is πr2.
•
The circumference of a circle is 2πr.
PLUGGING IN ON GEOMETRY PROBLEMS
Remember: Whenever you have a question that has answer choices, like a
regular multiple-choice question or a multiple-choice, multiple-answer
question that has variables in the answer choices, Plug In. On geometry
problems, you can plug in values for angles or lengths as long as the values
you plug in don’t contradict either the wording of the problem or the laws of
geometry (you can’t have the interior angles of a triangle add up to anything
but 180, for instance).
Here’s an example:
In the drawing above, if AC = CD, then r =
45 – s
90 – s
s
45 + s
60 + s
Here’s How to Crack It
See the variables in the answer choices? Let’s Plug In. First of all, we’re told
that AC and CD are equal, which means that ACD is an isosceles right
triangle. So angles A and D both have to be 45 degrees. Now it’s Plugging In
time. The smaller angles, r and s, must add up to 45 degrees, so let’s make r =
40 degrees and s = 5 degrees. The question asks for the value of r, which is
40, so that’s our target answer. Now eliminate answer choices by plugging in
5 for s.
(A) 45 − 5 = 40. Bingo! Check the other choices to be sure.
(B) 90 − 5 = 85. Nope.
(C) 5. Nope.
(D) 45 + 5 = 50. Eliminate it.
(E) 60 + 5 = 65. No way.
By the way, we knew that the correct answer couldn’t be greater than 45
degrees, because that’s the measure of the entire angle D, so you could have
eliminated (D) and (E) right away.
Don’t forget to Plug In on
geometry questions. Just
pick numbers according to
the rules of geometry.
DRAW IT YOURSELF
When ETS doesn’t include a drawing with a geometry problem, it usually
means that the drawing, if supplied, would make ETS’s answer obvious. In
cases like this, you should just draw it yourself. Here’s an example:
Quantity A
Quantity B
The diameter of a circle with
area 49π
14
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
Visualize the figure. If the area is 49π, what’s the radius? Right: 7. And if the
radius is 7, what’s the diameter? Right: 14. The answer is (C).
Redraw
On tricky quant comp questions, you may need to draw the figure once,
eliminate two answer choices, and then draw it another way to try to disprove
your first answer and to see if the answer is (D). Here’s an example of a
problem that might require you to do this:
D is the midpoint of AC.
Quantity A
Quantity B
m
n
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
For quant comp
geometry questions,
draw, eliminate, and
REDRAW; it’s like
Plugging In twice.
Here’s How to Crack It
Are you sure that the triangle looks exactly like this? Nope. We know only
what we are told—that the lengths of AD and DC are equal; from this figure,
it looks like angles m and n are also equal. Because this means that it’s
possible for them to be, we can eliminate (A) and (B). But let’s redraw the
figure to try to disprove our first answer.
Try drawing the triangle as stretched out as possible. Notice that n is now
clearly greater than m, so you can eliminate (C), and the answer is (D).
Geometry Drill
Think you have mastered these concepts? Try your hand at the following
problems and check your work after you have finished. You can find the
answers in Part V.
1 of 15
Which of the following could be the degree measures of two angles in a right triangle?
Indicate all such angles.
20° and 70°
30° and 60°
45° and 45°
55° and 55°
75° and 75°
2 of 15
What is the perimeter of the figure above?
51
64
68
77
91
3 of 15
AB = BC = EG
FG = 8
Quantity A
Quantity B
The area of square ABCD
32
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
4 of 15
(a, 6) is a point (not shown) in Quadrant I.
(–6, b) is a point (not shown) in Quadrant II.
Quantity A
Quantity B
a
b
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
5 of 15
A piece of twine with length of t is cut into two pieces. The length of the longer piece is 2 yards greater
than 3 times the length of the shorter piece. Which of the following is the length, in yards, of the longer
piece?
6 of 15
The circle with center D is drawn inside the circle with center C, as shown in the figure above. If CD =
3, what is the area of semicircle EAB ?
π
9π
12π
18π
36π
7 of 15
For the final exam in a scuba diving certification course, Karl navigates from one point in a lake to
another. Karl begins the test x meters directly beneath the boat and swims straight down toward the
bottom of the lake for 8 meters. He then turns to his right and swims in a straight line parallel to the
surface of the lake and swims 24 meters, at which point he swims directly from his location, in a
straight line, back to the boat. If the distance that Karl swims back to the boat is 26 meters, what is the
value of x ?
8 of 15
Quantity A
Quantity B
The circumference of a circular
region with radius r
The perimeter of a square with
side r
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
9 of 15
Triangle ABC is contained within a circle with center C. Points A and B lie on the circle. If the area of
circle C is 25π, and the measure of angle ACB is 60°, which of the following are possible lengths for
side AB of triangle ABC ?
Indicate all such lengths.
3
4
5
6
7
10 of 15
Quantity A is greater.
Quantity B is greater.
Quantity A
Quantity B
x
5.9
The two quantities are equal.
The relationship cannot be determined from the information given.
11 of 15
Quantity A
Quantity B
f
g
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
12 of 15
Given points A(2, 3) and B(x, y) in the rectangular coordinate system above, if y = 4.2, then x =
2.6
2.8
2.9
3.0
3.2
13 of 15
In rectangle ABCD above, which of the following is the area of the triangle ABD ?
6
7.5
10
12
15
14 of 15
The circle above has a center O.
∠AOB = ∠BOC
Quantity A
Quantity B
The area of triangle AOB
The area of the shaded region
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
15 of 15
The circumference of the circle with center O shown above is 15π. LMNO is a parallelogram and
∠OLM = 108°. What is the length of minor arc AB ?
15π
9π
3π
2π
π
Summary
There may only be a handful of geometry questions on the GRE, but
you’ll be expected to know a fair number of rules and formulas.
Line and angle problems typically test your knowledge of vertical
angles, parallel lines, right angles, and straight angles.
Triangles are a popular geometry topic on the GRE. Make sure you
know your triangle basics, including the total degrees of a triangle, the
relationship between the angles and sides of a triangle, and the third
side rule.
Right triangle problems frequently test the Pythagorean theorem and
the common Pythagorean triples 3 : 4 : 5 and 5 : 12 : 13.
Be aware of the two special right triangles that ETS likes to torture test
takers with: the 45 : 45 : 90 triangle and 30 : 60 : 90 triangle.
Know the area formulas for triangles, rectangles, squares, and circles.
Problems involving the xy-coordinate plane frequently test common
geometry concepts such as the area of a triangle or a square. Other
plane geometry questions will test you on slope and the equation of a
line.
Slope is defined as “rise over run.” Find it by finding the change in ycoordinates (the rise) and the change in x-coordinates (the run).
The equation of a line is y = mx + b, where x and y are the coordinates
of any point on the line, m is the slope and b is the y-intercept, the point
at which the line crosses the y-axis.
Don’t forget to Plug In on geometry problems!
Chapter 14
Math Et Cetera
There are a few more math topics that may appear on the GRE that don’t fit
nicely into the preceding chapters. This chapter looks at some of these
leftover topics, including probability, permutations and combinations, and
factorials. The topics in this chapter are not essential to your GRE Math score,
because these areas are not tested as frequently as the topics detailed earlier.
However, if you feel confident with the previous math topics, and you’re
looking to maximize your GRE Math score, this chapter will show you all
you need to know to tackle these more obscure GRE problems.
OTHER MATH TOPICS
The bulk of the GRE Math section tests your knowledge of fundamentals,
basic algebra, and geometry. However, there are a few other topics that may
appear. These “et cetera” concepts usually show up only once or twice per test
(although at higher scoring levels they may appear more frequently) and often
cause anxiety among test takers. Many test takers worry excessively about
probability problems, for example, even though knowledge of more familiar
topics such as fractions and percents will be far more important in
determining your GRE math score. So tackle these problems only after
you’ve mastered the rest. If you find these concepts more difficult, don’t
worry—they won’t make or break your GRE score.
These topics show up
rarely on the GRE, but if
you’re going for a very
high score, they are useful
to know.
PROBABILITY
If you flip a coin, what’s the probability that it will land heads up? The
probability is equal to one out of two, or . What is the probability that it
won’t land heads up? Again, one out of two, or . If you flip a coin nine
times, what’s the probability that the coin will land on heads on the tenth flip?
Still 1 out of 2, or . Previous flips do not affect the outcome of the current
coin flip.
You can think of probability as just another type of fraction. Probabilities
express a special relationship, namely the chance of a certain outcome
occurring. In a probability fraction, the denominator is the total number of
possible outcomes that may occur, while the numerator is the number of
outcomes that would satisfy the criteria. For example, if you have 10 shirts
and 3 of them are black, the probability of selecting a black shirt from your
closet without looking is
.
Since probability is
expressed as a fraction, it
can also be expressed as
a decimal or a percentage.
A probability of one-half is
equivalent to a probability
of 0.5 or 50%.
Think of probability in terms of fractions:
•
If it is impossible for something to happen—if no outcomes satisfy
the criteria—then the numerator of the probability fraction is 0 and
the probability is equal to 0.
•
If something is certain to happen—if all possible outcomes satisfy
the criteria—then the numerator and denominator of the fraction
are equal and the probability is equal to 1.
•
If it is possible for something to occur, but it will not definitely
occur, then the probability of it occurring is between 0 and 1.
probablity =
Let’s see how it works.
At a meeting of 375 members of a neighborhood association,
have lived in the community for less than 5 years and
of the participants
of the attendees have lived
in the neighborhood for at least 10 years. If a member of the meeting is selected at
random, what is the probability that the person has lived in the neighborhood for at
least 5 years but less than 10 years?
Here’s How to Crack It
In order to solve this problem, we need to put together our probability
fraction. The denominator of our fraction is going to be 375, the total number
of people from which we are selecting. Next we need to figure out how many
attendees satisfy the criteria of having lived in the neighborhood for more
than 5 years but fewer than 10 years.
What number goes on the
bottom of the probability
fraction?
First, we know that
less than 5 years.
running. Also,
10 years.
of the participants have lived in the neighborhood for
of 375 is 75 people, so we can take them out of the
of the attendees have lived in the neighborhood for at least
of 375 (be careful not to use 300 as the total!) is 250, so we can
also remove them from consideration. Thus, if 75 people have lived in the
neighborhood for less than 5 years and 250 have lived for at least 10, the
remaining people are the ones we want. 250 + 75 is 325, so that leaves us
with 50 people who satisfy the criteria. We need to make 50 the numerator of
our fraction, which gives us
. This reduces to
, and (A) is the answer.
Two Important Laws of Probability
When you want to find the probability of a series of events in a row, you
multiply the probabilities of the individual events. What is the probability of
getting two heads in a row if you flip a coin twice? The probability of getting
a head on the first flip is . The probability is also
that you’ll get a head on
the second flip, so the combined probability of two heads is
× , which
equals . Another way to look at it is that there are four possible outcomes:
HH, TT, HT, TH. Only one of those outcomes consists of two heads in a row.
Thus,
of the outcomes consist of two heads in a row. Sometimes the number
of outcomes is small enough that you can list them and calculate the
probability that way.
Probability of A and B
= Probability of A
× Probability of B
Occasionally, instead of finding the probability of one event AND another
event happening, you’ll be asked to find the probability of either one event
OR another event happening. In this situation, instead of multiplying the
probabilities, you add them. Let’s say you have a normal deck of 52 cards. If
you select a card at random, what’s the probability that you select a 7 or a 4?
The probability of selecting a 7 is
selecting a 4 is the same;
is
+
=
, which reduces to
. The probability of
. Therefore, the probability of selecting a 7 or a 4
.
Probability of A or B
= Probability of A
+ Probability of B
(The full formula for the
Probability of A or B
includes subtracting the
Probability of both A and
B, but the GRE only uses
mutually exclusive events,
so both A and B can’t
happen, and you don’t
need to worry about it!)
Let’s look at a problem:
When a pair of six-sided dice, each with faces numbered 1 to 6, is rolled once,
what is the probability that the result is either a 3 and a 4 or a 5 and a prime
number?
Give your answer as a fraction.
Here’s How to Crack It
Probability is fundamentally about counting. You need to be able to count all
the things that can happen and count all the situations that meet the conditions
of the problem. Sometimes, the easiest way to count both everything that can
happen and the situations that meet the condition is to write everything out. In
this case, let’s use a table:
Each cell of this table represents a result when the dice are rolled. For
example, the cell at the intersection of the row shown as 1 and the column
shown as 1 would represent that 1 was showing on each of the two die. This
cell has been marked with an because it does not meet either condition of
the problem.
The cells marked with a
are the only dice rolls that meet one of the
conditions of the problem. To finish, just count the
marks—there are 7.
(Remember that 1 is not prime. That’s why combinations such as 5 and 1 are
not checked.) Next, count the total possibilities—there are 36. So, the
probability of rolling either a 3 and a 4 or a 5 and prime number is
.
One last important thing you should know about probabilities is that the
probability of an event happening and the probability of an event not
happening must add up to 1. For example, if the probability of snow falling
on one night is , then the probability of no snow falling must be . If the
probability that it will rain is 80%, then the probability that it won’t rain must
be 20%. The reason this is useful is that, on some GRE probability problems,
it will be easier to find the probability that an event doesn’t occur; once you
have that, just subtract from 1 to find the answer.
Let’s look at the following example.
Dipak has a 25% chance of winning each hand of blackjack he plays. If he has
$150 and bets $50 a hand, what is the probability that he will still have money after
the third hand?
Since probabilities are just
fractions, they can also be
expressed as percents.
Here’s How to Crack It
If Dipak still has money after the third hand, then he must have won at least
one of the hands, and possibly more than one. However, directly calculating
the probability that he wins at least one hand is tricky because there are so
many ways it could happen (for example, he could lose-lose-win, or W-W-L
or W-L-W or L-W-L, and so on). So think about it this way: The question
asks for the probability that he will win at least one hand. What if he doesn’t?
That would mean that he doesn’t win any hands at all. If we calculate the
probability that he loses every hand, we can then subtract that from 1 and find
the corresponding probability that he wins at least one hand. Since Dipak has
a 25% chance of winning each hand, this means that he has a 75% chance of
losing it, or
(the answers are in fractions, so it’s best to work with
fractions). To find the probability that he loses all three hands, simply
multiply the probabilities of his losing each individual hand. × × =
there is a
, so
probability that he will lose all three hands. Subtracting this from
1 gives you the answer you’re looking for. 1 −
=
. The answer is (D).
Given events A and B, the probability of
•
A and B = (Probability of A) × (Probability of B)
•
A or B = Probability of A + Probability of B
Given event A
•
Probability of A + Probability of Not A = 1
FACTORIALS
The factorial of a number is equal to that number times every positive whole
number smaller than that number, down to 1. For example, the factorial of 6 is
equal to 6 × 5 × 4 × 3 × 2 × 1, which equals 720. The symbol for a factorial is
! so 4! doesn’t mean we’re really excited about the number 4, it means 4 × 3 ×
2 × 1, which is equal to 24. (0! is equal to 1, by the way.) When factorials
show up in GRE problems, always look for a shortcut like canceling or
factoring. The point of a factorial problem is not to make you do a lot of
multiplication. Let’s try one.
Quantity A
Quantity B
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
Let’s tackle Quantity A. We definitely don’t want to multiply out the
factorials since that would be pretty time-consuming: 12! and 11! are both
huge numbers. Instead let’s look at what they have in common. What we’re
really talking about here is
. Now
it’s clear that both factorials share everything from 11 on down to 1. The
entire bottom of the fraction will cancel and the only thing left on top will be
12, so the value of Quantity A is 12. For Quantity B, we can also write out the
factorials and get
. The 2 and the 1 in the bottom cancel, and the
only thing left on top will be 4 × 3, which is equal to 12. The two quantities
are equal and the answer is (C).
PERMUTATIONS AND COMBINATIONS
The basic definition of a permutation is an arrangement of things in a
particular order. Suppose you were asked to figure out how many different
ways you could arrange five statues on a shelf. All you have to do is multiply
5 × 4 × 3 × 2 × 1, or 120. (Yes, this is another application of factorials.) You
have five possible statues that could fill the first slot on the shelf, then, once
the first slot is filled, there are four remaining statues that could fill the second
slot, three that could fill the third slot, and so on, down to one.
Permutation problems
often ask for
arrangements, orders,
schedules, or lists.
Now suppose that there are five people running in a race. The winner of the
race will get a gold medal, the person who comes in second will get a silver
medal, and the person who comes in third will get a bronze medal. You’re
asked to figure out how many different orders of gold-silver-bronze winners
there can be. (Notice that this is a permutation because the order definitely
matters.)
First, ask yourself how many of these runners can come in first? Five. Once
one of them comes in first, she’s out of the picture, so how many can then
come in second? Four. Once one of them comes in second, she’s out of the
picture, so how many of them can come in third? Three. And now you’re
done because all three slots have been filled. The answer is 5 × 4 × 3, which
is 60.
To solve a permutation
•
Figure out how many slots you have.
•
Write down the number of options for each slot.
•
Multiply them.
The difference between a permutation and a combination is that in a
combination, the order is irrelevant. A combination is just a group, and the
order of elements within the group doesn’t matter. For example, suppose you
were asked to go to the store and bring home three different types of ice
cream. Now suppose that when you got to the store, there were five flavors in
the freezer—chocolate, vanilla, strawberry, butter pecan, and mocha. How
many combinations of three ice cream flavors could you bring home? Notice
that the order doesn’t matter, because bringing home chocolate, strawberry,
and vanilla is the same thing as bringing home strawberry, vanilla, and
chocolate. One way to solve this is the brute force method; in other words,
write out every combination.
VCS VCB VCM VSB VSM VBM CSB CSM CBM SBM
Combination problems
usually ask for groups,
teams, or committees.
That’s 10 combinations, but there’s a quicker way to do it. Start by filling in
the three slots as you would with a permutation (there are three slots because
you’re supposed to bring home three different types of ice cream). Five
flavors could be in the first slot, four could be in the second, and three could
be in the third. So far, that’s 5 × 4 × 3. But remember, this takes into account
all the different orders that three flavors can be arranged in. We don’t want
that, because the order doesn’t matter in a combination. So we have to divide
5 × 4 × 3 by the number of ways of arranging three things. In how many ways
can three things be arranged? That’s 3!, 3 × 2 × 1, which is 6. Thus we end up
with
. Cancel the denominators, to find that all that remains is 5 × 2 =
10. Bingo.
Does the order matter?
To solve a combination
•
Figure out how many slots you have.
•
Fill in the slots as you would a permutation.
•
Divide by the factorial of the number of slots.
The denominator of the fraction will always cancel out completely, so
it’s best to try and cancel first before you multiply.
Here’s an example:
Brooke wants to hang three paintings in a row on her wall. She has six paintings to
choose from. How many arrangements of paintings on the wall can she create?
6
30
90
120
720
Always cross off wrong
answer choices on your
scratch paper.
Here’s How to Crack It
The first thing you need to do is determine whether the order matters. In this
case it does, because we’re arranging the paintings on the wall. Putting the
Monet on the left and the Van Gogh in the middle isn’t the same arrangement
as putting the Van Gogh on the left and the Monet in the middle. This is a
permutation question. We have three slots to fill because we’re arranging
three paintings. There are 6 paintings that could fill the first slot, 5 paintings
that could fill the second slot, and 4 paintings that could fill the third slot. So
we have 6 × 5 × 4, which equals 120. Thus, the correct answer is (D).
Here’s another example:
A pizza may be ordered with any of eight possible toppings.
Quantity A
Quantity B
The number of different ways
to order a pizza with three
different toppings
The number of different ways
to order a pizza with five
different toppings
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
First, note that for both quantities we’re dealing with a combination, because
the order of toppings doesn’t matter. A pizza with mushrooms and pepperoni
is the same thing as a pizza with pepperoni and mushrooms. Let’s figure out
Quantity A first.
We have eight toppings and we’re picking three of them. That means we have
three slots to fill. There are 8 toppings that could fill the first slot, 7 that could
fill the second slot, and 6 that could fill the third, so we have 8 × 7 × 6. Since
this is a combination, we have to divide by the factorial of the number of
slots. In this case we have three slots, so we have to divide by 3!, or 3 × 2 × 1.
So our problem looks like this:
. To make the multiplication easier,
let’s cancel first. The 6 on top will cancel with the 3 × 2 on the bottom,
leaving us with
, which is 56. Thus, there are 56 ways to order a three-
topping pizza with eight toppings to choose from. Now let’s look at Quantity
B.
We still have eight toppings, but this time we’re picking five of them so we
have five slots to fill. There are 8 toppings that could fill the first slot, 7 that
could fill the second slot, 6 that could fill the third, 5 that could fill the fourth,
and 4 that could fill the fifth. That’s 8 × 7 × 6 × 5 × 4, but we still have to
divide by the factorial of the number of slots. We have five slots, so that
means we need to divide by 5!, or 5 × 4 × 3 × 2 × 1. Thus we have
. We definitely want to cancel first here, rather than doing all
that multiplication. The 5 on top will cancel with the 5 on the bottom.
Likewise, the 4 on top will cancel with the 4 on the bottom. The 6 on top will
cancel with the 3 × 2 on the bottom, leaving us again with
, which is 56.
Therefore, there are also 56 ways to order a five-topping pizza with eight
toppings to choose from. The two quantities are equal, and the answer is (C).
Let’s try one more:
Nicole needs to form a committee of 3 from a group of 8 research attorneys to
study possible changes to the Superior Court. If two of the attorneys are too
inexperienced to serve together on the committee, how many different
arrangements of committees can Nicole form?
20
30
50
56
336
Here’s How to Crack It
This problem is a little more complicated than an ordinary combination
problem, because an extra condition has been placed on the committee.
Without that condition, this would be a fairly ordinary combination problem,
and we’d simply calculate how many groups of three can be created with
eight people to choose from.
There’s more than one way to approach this problem. First, you should realize
that there are two ways that we could form this committee. We could have
three experienced attorneys, or we could have two experienced attorneys and
one inexperienced attorney. If we find the number of ways to create each of
those two possibilities, we can add them together and have our answer. It’s
fairly straightforward to calculate the number of ways to have three
experienced attorneys on a committee: There are three slots to fill, and we
have 6 options for the first slot, 5 for the second, and 4 for the third. Here the
order doesn’t matter, so we divide by 3! to get
= 20. Thus there are
20 ways to create the committee using three experienced attorneys. What
about creating a committee that has two experienced attorneys and one
inexperienced attorney? We have 6 options for the first experienced attorney
and 5 options for the second. Order doesn’t matter so we divide by 2!. So far
we have
. Next we have 2 options for the inexperienced attorney, so now
we have to multiply by 2, and our calculation is
= 30. As you can
see, there are 30 ways to create the committee using two experienced
attorneys and one inexperienced attorney. Adding 20 and 30 gives us 50 total
committees, and the answer is (C).
Here’s another way that you could solve the problem. If there were no
conditions placed on the committee, we could just calculate
, which
would give us 56 committees. But we know some of those committees are not
allowed; any committee that has the two inexperienced attorneys on it isn’t
allowed. How many of these types of committees are there? Let’s call the
inexperienced attorneys A and B. An unacceptable committee would be A B
__, in which the last slot could be filled by any of the experienced attorneys.
Since there are 6 experienced attorneys, there are 6 unacceptable committees.
Subtracting them from 56 gives us 50 acceptable committees. Hey, the
answer’s still (C)!
FUNCTIONS AND THE GRE
f(x) Notation
ETS often employs the use of function notation to create difficult problems.
Generally speaking, the function notation is a style of math problem that
causes test takers to be nervous. The function notation, ƒ(x), is unfamiliar to
look at, seems difficult and involved, and evokes memories of graphs and
charting lines that you may have learned in high school geometry.
The good news is that pure function problems on the GRE are much more
straightforward than that and become very manageable if you utilize Plugging
In strategies.
The easiest way to think about a function question is to look at an example.
Take ƒ(x) = x + 2, for instance. All this problem is stating is that for any value
of x, the function ƒ(x) is that value plus 2. Let’s say that x = 3; therefore, to
solve this problem, take the value of x and plug it into the given equation. So
if x = 3, the equation now reads ƒ(3) = 3 + 2, or ƒ(3) = 5. To solve function
notation problems, all you need to do is read the instructions carefully and fill
in the values for the variables where appropriate. If you used the same
equation, but the value of x is 10, then the function is now ƒ(10) = 10 + 2, so
ƒ(10) = 12.
Sometimes a function problem gives a restriction such as x ≠ 0. If this is the
case, you know that x could be equal to any value but 0, and this is generally
for a good reason. If ƒ(x) = , then x cannot equal 0 because a number cannot
be divided by 0.
Try this example of a function question on the GRE.
If − 3 ≤ g ≤2 and f(g) = −2g and g is an integer, then which of the following
integers could be a value of f(g) ?
Indicate all such integers.
–6
–5
–2
0
2
4
6
Here’s How to Crack It
This is a function problem with restrictions, so find all the different values
that can be plugged in for g. Since g is an integer that is equal to or between
−3 and 2 then there is a range for its values. Therefore, ƒ(g) (which equals
−2g) is all the integer values between the high and low end of the range of g
multiplied by 2. In other words, plug in 2 and −3 for g in the function and
figure out what the range is. If g = −3, then ƒ(g) is ƒ(–3)= −2(–3) = 6. And if
g = 2, then ƒ(g) is f(2) = −2(2) = −4. So the range of ƒ(g) is −4 ≤ ƒ(g) ≤ 6.
Choices (A) and (B) are less than −4 and fall out of the range. The rest of the
integers fall in the range, so they are possible values of ƒ(g). Therefore the
correct answer is (C), (D), (E), (F), and (G).
Evaluating functions is all about following the directions. Just plug in the
values for the variable and solve.
Functions With Uncommon Symbols:
The GRE also tries to scare students using functions in another way: picking
strange symbols and putting them in a problem. When you see a funny
symbol that you have never seen before, don’t stress out! It’s just a function
problem in disguise. Follow the directions to find the correct answer.
A problem with funny symbols may look something like the following.
If the operation is defined for all integers x and y as x
which of the following is equal to 4 −3 ?
y = x 2 + y − 2, then
21
17
15
11
10
Here’s How to Crack It
Remember, this is a function problem, so just follow the directions. The
problem wants to know the value of 4 −3, and it states that x y = x2 + y −
2. To solve this problem, plug in x = 4 and y = −3. So 4 −3 = 42 + (–3) − 2.
Now, solve: 4 −3 = 16 − 3 − 2 = 11. The correct answer is (D).
You may get a different symbol when you get another problem like this, but
the process is still the same. Just plug in the values given for the variables and
solve the problem. If you have worked your way through this book and
mastered the content, then there won’t be any actual mathematical symbols on
the GRE that are unfamiliar to you. If you see a symbol like that, it’s a
function problem!
Let’s look at one more example.
For any non-negative integer x, let x* = x − 1.
Quantity A
Quantity B
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Here’s How to Crack It
Just follow the directions: 15* = 15 − 1, or 14, and 3* = 3 − 1, or 2. So
Quantity A is
, or 7. Don’t forget PEMDAS for Quantity B. First,
is 5.
Then, 5* = 5 − 1, or 4. So because Quantity A is 7 and Quantity B is 4, the
correct answer is (A).
GROUPS
Group problems, although not too common on the GRE, can be troublesome
if you don’t know how to set them up. When confronted by a group problem,
use the group equation
T = G1 + G2 – B + N
You might see one group
problem on the GRE.
In the equation, T represents the Total, G1 is one group, G2 is the second
group, B is for the members in both groups and N is for the members in
neither group. Here’s an example of a typical group problem.
A biologist studying breeding groups noted that of 225 birds tagged for the study,
85 birds made nests in pine trees, 175 made nests in oak trees, and 40 birds did not
build nests in either type of tree. How many birds built nests in both types of trees?
45
60
75
80
125
Wrapping Up Math
You’re almost done with
the Math section. Tackle
the Math Drills on the
following pages, then give
yourself a break before
you dive into the
Analytical Writing
Section. Take a walk, eat
a snack, or meet up with a
pal and give youself some
downtime before you dive
into Part IV.
Here’s How to Crack It
Let’s use the group equation. The total is 225, one group consists of 85 birds,
the other group has 175 birds in it, and we know that 40 birds built nests in
neither type of tree. Our equation would look like this:
225 = 85 + 175 – B + 40
All we have to do is solve for B. Simplifying the equation gives us 225 = 300
– B, so B must equal 75. Choice (C) is our answer.
Et Cetera Drill
Here are some math questions to practice on. Remember to check your
answers when you finish. You can find the answers in Part V.
1 of 10
A bowl contains 15 marbles, all of which are either red or blue. If the number of red marbles is one
more than the number of blue marbles, what is the probability that a marble selected at random is blue?
2 of 10
If ¥(x) = 10x − 1, what is ¥(5) – ¥(3) ?
15
18
19
20
46
3 of 10
For all positive integer values of x, #x = 2–x.
Quantity A
Quantity B
#8
#4
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
4 of 10
At a recent dog show, there were 5 finalists. One of the finalists was awarded “Best in Show” and
another finalist was awarded “Honorable Mention.” In how many ways could the two awards be given
out?
5 of 10
Company X budgets $90,000 total on advertising for all of its products per year. Company X budgets
$40,000 for all advertising for product A and $30,000 for all advertising for product B. From the budgets
for products A and B, $15,000 is budgeted for advertisements that feature both products used as a
system.
Quantity A
Quantity B
The total amount Company X
budgets for advertising
products other than products A
and B.
$20,000
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
6 of 10
Lee randomly selects a 2-digit prime number less than 50. What is the probability that the tens digit is
greater than the units digit?
7 of 10
An elected official wants to take five members of his staff to an undisclosed secure location. What is the
minimum number of staff members the elected official must employ in order to have at least 20
different groups that could be taken to the location?
7
8
9
10
11
8 of 10
For all real numbers x and y, if x # y = x(x – y), then x # (x # y) =
x2 – xy
x2 − 2xy
x3 – x2 – xy
x3 – (xy)2
x2 – x3 + x2y
9 of 10
A jar contains 12 marbles. Each is either yellow or green and there are twice as many yellow marbles as
green marbles. If two marbles are to be selected from the jar at random, what is the probability that
exactly one of each color is selected?
10 of 10
A set of 10 points lies in a plane such that no three points are collinear.
Quantity A
The number of distinct
triangles that can be created
from the set
Quantity B
The number of distinct
quadrilaterals that can be
created from the set
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Comprehensive Math Drill
Let’s do a drill involving all of the math topics we have covered throughout
the book. Remember to check your answers when you finish. You can find the
answers in Part V.
1 of 20
Line AB is tangent to the circle C at point A. The radius of the circle with center C is 5 and BC =
Quantity A
Quantity B
The length of line segment AB
The length of line segment AC
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
2 of 20
x≠0
Quantity A
Quantity B
.
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
3 of 20
The test scores for a class have a normal distribution, a mean of 50, and a standard deviation of 4.
Quantity A
Percentage of scores at or
above 58
Quantity B
Percentage of scores at or
below 42
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
4 of 20
The line y = − x + 1 is graphed on the rectangular coordinate axes.
Quantity A
Quantity B
OQ
OP
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
5 of 20
At a dog show, there are 20 judges and 10 dogs in the final round.
Quantity A
Quantity B
The number of distinct pairs of
judges
The number of possible
rankings of dogs from first to
third place
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
6 of 20
k>0
l>1
Quantity A
Quantity B
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
7 of 20
Quantity A
The greatest odd factor of 78
Quantity B
The greatest prime factor of 78
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
8 of 20
Joe has $200. If he buys a CD player for $150, what is the greatest number of CDs he can buy with the
remaining money if CDs cost $12 each?
9 of 20
What is the area of triangle ABC in the figure above?
2
4
4
7
8
10 of 20
By which of the following could 10(96) be divided by to produce an integer result?
Indicate all such values.
90
100
330
540
720
11 of 20
Roberta drove 50 miles in 2 hours. Her rate in miles per hour is equivalent to which of the following
proportions?
Indicate all such proportions.
5 to 20
100 to 4
400 to 16
20 to 500
520 to 20
Questions 12 through 14 refer to the following graph.
12 of 20
For how many of the cities shown was the highest temperature in Year Y greater than or equal to the
highest temperature in Year X ?
4
5
7
8
12
13 of 20
What is the approximate percent increase from the lowest average (arithmetic mean) temperature for
Years X and Y to the highest average temperature?
60%
82%
140%
188%
213%
14 of 20
The average (arithmetic mean) temperature for any city in Years X and Y is the average of the high and
low temperatures for those years. What is the average of the low temperatures for Baltimore for Years X
and Y ?
−9° F
11° F
20° F
44° F
It cannot be determined from the information given.
15 of 20
If |2x − 3| + 2 > 7, which of the following could be the value of x ?
Indicate all such values.
–4
–3
–2
–1
0
1
2
3
16 of 20
If x, y, and z are consecutive odd integers where x < y < z and x + y + z < z, then which of the following
could be the value of x ?
Indicate all such values.
–3
–1
0
1
3
17 of 20
If 4x = 1,024, then (4x + 1)(5x – 1) =
106
(54)(105)
(44)(105)
(54)(104)
(44)(104)
18 of 20
What is the greatest distance between two vertices of a rectangular solid with a height of 5, a length of
12, and a volume of 780 ?
12
12
13
13
13
19 of 20
If three boys and three girls sit in a row on a park bench, and no boy can sit on either end of the bench,
how many arrangements of the children on the bench are possible?
46,656
38,880
1,256
144
38
20 of 20
If 16 is the average (arithmetic mean) of p, 24, and q, what is 16(p + q) ?
180
192
384
524
768
Summary
Topics such as probability, permutations and combinations, factorials,
and functions represent only a small percentage of the math topics
tested on the GRE. Make sure you’ve mastered all the more important
topics before attempting these.
Probability is expressed as a fraction. The denominator of the fraction
represents the total number of possible outcomes, while the numerator
stands for the desired outcomes.
If a probability question asks for the chance of event A or event B, find
the probability of each event and add them together. If the question asks
for the probability of event A and event B, multiply the individual
probabilities.
The key to factorial problems is to look for ways to cancel or factor out
terms.
Permutations and combinations are related concepts. A permutation
tells you how many arrangements or orderings of things are possible. A
combination tells you how many groupings of things are possible.
Function problems use funny looking symbols as shorthand for the
operations to perform on a certain number.
The group equation is Total = Group1 + Group2 – Members of Both
Groups + Members of Neither Group.
Part IV
How to Crack the Analytical
Writing Section
15 The Writing Section
16 The Issue Essay
17 The Argument Essay
Chapter 15
The Geography of the Analytical
Writing Section
This chapter clues you in on everything you’ve ever wanted to know about
the Analytical Writing section of the GRE. It contains important information
on how the essays are used by graduate schools, the scoring system ETS
graders use to evaluate your essays, and the crucial distinctions between the
issue essay and the argument essay. This chapter also looks at the basic wordprocessing program used by ETS.
ESSAYS AND THE GRE
The Analytical Writing section of the GRE requires you to write two essays—
one will be an analysis of an issue and the other will be an analysis of an
argument. You will have 30 minutes for each essay.
In the past, ETS has had problems with test takers relying on preplanned
essays. The essay questions have been reformulated to reduce the possibility
of testers preparing their essays in advance. However, while you may not be
able to plan your entire essay in advance, you can still go into your test
session having a good idea of what type of essay you’re going to write.
How Do Schools Use the Writing Assessment?
First, the essays are probably more important for international students and
those for whom English is not a first language. If you are not a native English
speaker, expect your essay score and the essays you wrote to receive more
attention. (ETS also makes the essays available to schools, which may choose
to read them or not.) Second, and not surprisingly, the essays will probably be
weighted more heavily by programs for which writing is a frequent and
necessary task. A master’s program in applied mathematics might not care so
much about your 30-minute written opinion about whether or not it’s
necessary for a person to read imaginative literature, but a program in creative
writing probably would.
Even if your program
doesn’t care much about
the essay, a poor score
might still raise a red flag.
Ultimately, though, here’s the most honest answer to this question: It depends.
Some schools will not care at all about the Analytical Writing score, while
others will say that they want only applicants who scored a 5 or higher on this
section. Call the schools you’re interested in and talk to people in the
department. By finding out how important your target schools consider the
Analytical Writing section, you’ll be able to determine the appropriate
amount of effort to devote to it.
Regardless of your target score on this section, you should at least read
through these chapters to get a better sense of what ETS is looking for. You’ll
have to write these essays, so no matter what, you want to do a decent job.
You’ll find that writing high-scoring essays is not as hard as it may seem once
you’ve been shown how to do it.
More Online!
Head over to
PrincetonReview.com/gradschool-advice for useful
information and helpful
articles about
graduate school.
How Will the Essays Be Scored?
Your essays will be read by two graders, and each will assign a score from 1
to 6, based on how well you do the following:
What you write—the
content—will be
weighted more than
how you write.
•
follow the instructions of the prompt
•
consider the complexities of the issue or argument
•
effectively organize and develop your ideas
•
support your position with relevant examples
•
control the elements of written English
The grades you receive for each essay will be totaled and averaged. For
example,
if you receive a 4 and a 5 on your issue essay and a 3 and a 4 on your
argument
essay, your Analytical Writing score will be a 4.0; 16 total points divided by 4
scores. If the graders’ scores for your essays differ by more than one point, a
third person will be brought in to read the essay. The graders use a holistic
grading system; they’re trained to look at the big picture, not to focus on
minor details. Your essay is not expected to be perfect, so the graders will
overlook minor errors in spelling, punctuation, and grammar. However,
pervasive or egregious errors will affect your score.
Here are ETS’s descriptions of the scoring levels:
Issue Essay
6
An essay that scores a 6 presents a cogent, well-articulated critique of
the issue and conveys meaning skillfully.
5
An essay that scores a 5 presents a generally thoughtful, welldeveloped analysis of the complexities of the issue and conveys
meaning clearly.
4
An essay that scores a 4 presents a competent analysis of the issue
and conveys meaning adequately.
3
An essay that scores a 3 demonstrates some competence in its
analysis of the issue and in conveying meaning but is obviously
flawed.
2
An essay that scores a 2 demonstrates serious weaknesses in
analytical writing.
1
An essay that scores a 1 demonstrates fundamental deficiencies in
analytical writing skills.
Argument Essay
6
An essay that scores a 6 presents a cogent, well-articulated critique of
the argument and conveys meaning skillfully.
5
An essay that scores a 5 presents a generally thoughtful, welldeveloped critique of the argument and conveys meaning clearly.
4
An essay that scores a 4 presents a competent critique of the
argument and conveys meaning adequately.
3
An essay that scores a 3 demonstrates some competence in its
critique of the argument and in conveying meaning but is obviously
flawed.
2
An essay that scores a 2 demonstrates serious weaknesses in
analytical writing.
1
An essay that scores a 1 demonstrates fundamental deficiencies in
both analysis and writing.
An essay written on a topic other than the one provided will receive a score of
0.
Who Are These Readers Anyway?
We’ll put this in the form of a multiple-choice question:
Your essays will initially be read by
(A) captains of industry
(B) leading professors
(C) college TAs working part time
If you guessed (C), you’re correct. Each essay will be read by part-time
employees of ETS, mostly culled from graduate school programs.
How Much Time Do They Devote to Each
Essay?
The short answer is this: not much. It is unusual for a grader to spend more
than two minutes grading an essay, and some essays are graded in less than a
minute. The graders are reading many, many GRE essays and they aren’t
going to spend time admiring that clever turn of phrase you came up with. So
don’t sweat the small stuff—it probably won’t even be noticed. Focus on the
big picture—that’s what the graders will be focusing on.
ETS graders spend less
than two minutes
grading your essay.
So How Do You Score High on the Analytical
Writing Essays?
On the face of it, you might think it would be pretty difficult to impress these
jaded readers, but it turns out that there are some very specific ways to
persuade them of your superior writing skills.
Make the graders’ jobs
easy. Give them exactly
what they’re looking for.
What ETS Doesn’t Want You to Know
In a recent analysis of a group of essays written by actual test takers, and the
grades that those essays received, ETS researchers noticed that the most
successful essays had one thing in common. Which of the following
characteristics do you think it was?
•
good organization
•
proper diction
•
noteworthy ideas
•
good vocabulary
•
sentence variety
•
length
What Your Essay Needs in Order to Look Like
a Successful Essay
The ETS researchers discovered that the essays that received the highest
grades from ETS essay graders had one single factor in common: length.
To ace the Analytical Writing section, you need to take one simple step: Write
as much as you possibly can. Each essay should include at least four indented
paragraphs. Your Issue essay should be 400 to 750 words in length, and your
Argument essay should be 350 to 600 words.
So All I Have to Do Is Type “I Hate the GRE”
Over and Over Again?
Well, no. The length issue isn’t that easy. The ETS researchers also noted that,
not surprisingly, the high-scoring essays all made reasonably good points
addressing the topic. So you have to actually write something that covers the
essay topic. And in your quest for length, it’s more important that you add
depth than breadth. What this means is that it’s better to have a few good
examples that are thoroughly and deeply explored than it is to add length by
tacking more and more examples and paragraphs onto your essay until it
starts to feel like a superficial list of bulleted points rather than a thoughtful
piece of writing.
Read the Directions Every Time
You should read the directions for each essay prompt. The instructions we
provide here for each essay task are not necessarily the ones you will see on
the GRE. Directions can vary in focus, so you shouldn’t memorize any
particular set of instructions. Visit the ETS website at www.ets.org/gre for a
complete list of all the potential essay topics and direction variants. (Yes, you
really get to see this information in advance of the test!) Practice responding
to the different instructions, combined with a variety of issue and argument
prompts. Be sure to mix it up; the prompt/directions pairings you see on the
ETS website are not necessarily the duos you will see on the real test.
Practicing with a variety of these essays will prepare you for whatever comes
your way on test day.
Oh, Yes, You Can Plan Your Essays in
Advance
In fact, there are some very specific ways to prepare for the essays that go
beyond length and good typing skills. So how can you prepare ahead of time?
Creating a Template
When a builder builds a house, the first thing he does is construct a frame.
The frame supports the entire house. After the frame is completed, he can nail
the walls and windows to the frame. We’re going to show you how to build
the frame for the perfect GRE essay. Of course, you won’t know the exact
topic of the essay until you get there (just as the builder may not know what
color his client is going to paint the living room), but you will have an allpurpose frame on which to construct a great essay no matter what the topic is.
We call this frame the template.
Preconstruction
Just as a builder can construct the windows of a house in his workshop weeks
before he arrives to install them, so can you pre-build certain elements of your
essay. We call this “preconstruction.”
In the next two chapters we’ll show you how to prepare ahead of time to write
essays on two topics that you won’t see until they appear on your screen.
ISSUE VERSUS ARGUMENT ESSAY
It is worth noting at this time that the essay section gives you two very
distinct writing tasks, and that a failure to appropriately address these tasks
will severely reduce your score.
The Issue Essay
The Issue essay asks for your opinion; you’re expected to present your
viewpoint on a particular topic and support that viewpoint with various
examples. The following is one example of the instructions for the Issue
essay:
You will be given a brief quotation that states or implies an issue of general interest
and specific instructions on how to respond to that issue. You will have 30 minutes
to plan and compose a response in which you develop a position on the issue
according to the specific instructions. A response to any other issue will receive a
score of zero.
Make sure that you respond to the specific instructions and support your position
on the issue with reasons and examples drawn from such areas as your reading,
experience, observations, and/or academic studies.
Note how important it is to specifically address the assignment provided as
part of the Issue prompt; not following ETS’s directions will make your
grader unhappy and result in a poor score on the essay.
The Argument Essay
The Argument essay requires a different type of response. Instead of
presenting your own perspective, your job is to critique someone else’s
argument. You’re supposed to address the logical flaws of the argument, not
provide your personal opinion on the subject. The following is one example
of the directions for the Argument essay:
You will be given a short passage that presents an argument, or an argument to be
completed, and specific instructions on how to respond to that passage. You will
have 30 minutes to plan and compose a response in which you analyze the passage
according to the specific instructions. A response to any other argument will
receive a score of zero.
Note that you are NOT being asked to present your own views on the subject.
Make sure that you respond to the specific instructions and support your analysis
with relevant reasons and/or examples.
In the Argument essay, the emphasis is on writing a logical analysis of the
argument, not an opinion piece. It is absolutely essential that you don’t
confuse the two essay tasks on the GRE.
ETS graders don’t expect a
perfect essay; occasional
spelling, punctuation,
and grammar errors won’t
kill your score.
HOW DOES THE WORD-PROCESSING
PROGRAM WORK?
ETS has created a very simple program that allows students to compose their
essays on the screen. Compared to any of the commercial word-processing
programs, this one is extremely limited, but it does allow the basic functions:
You can move the cursor with the arrow keys, and you can delete, copy, and
paste. You don’t have to use any of these functions. With just the backspace
key and the mouse to change your point of insertion, you will be able to use
the computer like a regular word-processing program.
Take a look at the image below to see what your screen will look like during
the Analytical Writing section of the test:
The question will always appear at the top left of your screen. Beside it, in a
box, will be your writing area (in the writing area above, you can see a
partially completed sentence). When you click inside the box with your
mouse, a winking cursor will appear, indicating that you can begin typing.
As we said above, the program supports the use of many of the normal
computer keys.
•
The “Backspace” key removes text to the left of the cursor.
•
The “Delete” key removes text to the right of the cursor.
•
The “Arrow” keys move the cursor up, down, left, or right.
•
The “Home” key moves the cursor to the beginning of a line.
•
The “End” key moves the cursor to the end of a line.
•
The “Enter” key moves the cursor to the beginning of the next
line.
•
“Page up” moves the cursor up one page.
•
“Page down” moves the cursor down one page.
You can also use the buttons above the writing area to copy and paste words,
sentences, or paragraphs. To do this, you first have to highlight the desired
text by clicking on the starting point with your mouse and holding down the
mouse button while you drag it to the ending point. Then click on the “Cut”
button. This deletes the text you’ve selected from the screen, but also stores it
in the computer’s memory. Next, just move the cursor to wherever you would
like the selected text to reappear, and click on the “Paste” button. The selected
text will appear in that spot.
If you make a mistake, simply click on the “Undo” button, which will undo
whatever operation you have just done. You can undo a cut, a paste, or even
the last set of words you’ve typed in. Unfortunately, unlike many wordprocessing programs, ETS’s program does not have a “Redo” button, so be
careful what you decide to undo.
Obviously, the small box on the screen is not big enough to contain your
entire essay. However, by hitting the “Page up” and “Page down” keys on
your keyboard, or by using the arrows on your keyboard, you will be able to
go forward and backward to reread what you have written and make
corrections.
Does Spelling Count?
Officially, no. The word-processing program doesn’t have a spell checker, and
ETS essay readers are supposed to ignore minor errors of spelling and
grammar, but the readers wouldn’t be human if they weren’t influenced by an
essay that had lots of spelling mistakes and improper grammar—it gives the
impression that you just didn’t care enough to proofread.
Because pervasive spelling errors will detract from your score, pick an easier
word if you’re really uncertain of how to spell a word.
Summary
Different programs value the essay section in different ways. Check
with your program to see how important the essays are.
Understand the criteria ETS uses for judging your essay. Organization,
examples, and language use are important. Perfect grammar and
spelling less so.
On the GRE, longer essays tend to receive better scores, so strive to
write as much as you can for each essay.
Make sure you understand the differences in the assignments for the
Issue essay and the Argument essay.
Issue essays ask for your opinion on a topic while Argument essays
expect you to critique the logic of an argument. The ways in which
you’re asked to do each of these tasks will vary, so make sure you read
each set of directions carefully.
The word processor ETS provides has only the most basic functions.
You can delete, copy, and paste text, but not much more.
Chapter 16
The Issue Essay
The Issue essay of the GRE requires you to present your opinion on the
provided topic. This chapter will show you the steps to take in order to write a
clear, coherent essay in the limited time provided. You’ll learn the key parts
of a successful essay, and how to brainstorm ideas, combine them into a
thesis, and then structure a cohesive essay that will get you the best possible
result.
THREE BASIC STEPS
Because you don’t have a lot of time to write the essays, you’ll need to have a
pretty good idea of how you’re going to attack them as soon as you sit down
at the computer on test day. Our approach to the essays involves three steps:
1. Think. Before you start writing, take a moment to brainstorm some
thoughts about the topic.
2. Organize. Take the ideas you’ve come up with and fit them into
the assignment for the prompt.
3. Write. Once you’ve completed the first two steps, the final step
should be a snap.
Thirty minutes is not a lot of time to write an essay, so you have to get it right
the first time out. While ETS advises you to leave enough time to proofread
and edit your essay, it simply isn’t feasible to expect to make any significant
changes to your essay during the final minutes of the section. Furthermore, if
you get halfway through your essay and realize you’re stuck or you’re not
saying what you need to say, you’ll be hard pressed to fix your essay in the
time you have left.
It is essential, therefore, to make sure you spend time planning your essay
before you start writing. You have to figure out what it is you want to say
before you begin; otherwise, you run the risk of writing an incoherent,
rambling essay. The first two steps are actually more important to a successful
GRE essay than the final step; by spending a little time planning your essay,
the actual writing part should be relatively painless.
The keys to the essay: Think, Organize, Write
You have to know what
you want your essay to
say before you can
start writing.
Essay Essentials
As you learned in sixth-grade composition class, a basic essay has three parts:
an introduction, some body paragraphs, and a conclusion. These three things
are exactly what you should include in your Analysis of an Issue Essay. Each
of these parts has a specific role to play.
1. The introduction should introduce the topic of the essay, discuss
the issues surrounding it, and present the essay’s thesis.
2. The body paragraphs should use examples to support the thesis of
the essay.
3. The conclusion should summarize the major points of the issue,
reiterate the thesis, and perhaps consider its implications.
Basically, if you try to think of each paragraph as having a specific job to do,
you can pretty much preconstruct each type of paragraph and then fill in the
specific details on test day.
The basics parts of
an essay include the
introduction, body
paragraphs, and
conclusion.
Keys to a High-Scoring Essay
In order to write a high-scoring Issue essay, you’ll want to accomplish four
key tasks. A high-scoring Issue essay
•
considers the complexities of the issue
•
supports the position with relevant examples
•
is clear and well organized
•
demonstrates superior facility with the conventions of standard
written English
To put it more simply, your essay should be logically organized, include good
examples to support whatever position you’ve taken, and demonstrate that
you can use the English language reasonably well in writing.
Let’s continue our discussion of the Issue essay by looking at a typical
prompt.
The Prompt
“True beauty is found not in the exceptional but in the commonplace.”
Write an essay in which you take a position on the statement above. In developing and supporting
your essay, consider instances in which the statement does and does not hold true.
The prompts are supposed to get you thinking about areas of “general
interest,” whatever that means. A better way of thinking about the prompt is
to look at it as an agree/disagree or pro/con statement. Your task in the essay
will be to look at both sides of the issue, the pro and the con side, and take a
position on the statement. Let’s look at how to do that.
STEP 1: THINK
“Think” is a pretty broad command, so we need to clarify this step in order to
make it more useful. Specifically, we want you to think about three things.
1. Key Terms. What are the key words or phrases in the prompt? Do
the terms need clarifying before you can properly deal with them in
the essay?
2. Opposite Side. What would the converse of the statement be?
3. Examples. What are some examples that would support the
statement? What are some examples that would support the
opposite statement?
Let’s work through these steps with our sample prompt.
Key Terms
When preparing your essay, first look more closely at the key terms in the
prompt. Do they need to be clarified? Are there multiple ways of interpreting
the words? In order to make your essay as focused as possible, you might
need to limit the key terms to a specific definition or interpretation. If the key
terms in the prompt seem pretty straightforward, you still want to note them.
By repeatedly returning to these terms in your essay, you’ll convey the
impression that your essay is strongly organized and on topic.
For the sample prompt above, write down the key terms on a separate sheet of
scratch paper.
For this prompt, the key terms are beauty, true, exceptional, and
commonplace. We need to think about how we’re going to use these terms in
our essay. For example, what is true beauty? Do we want that to mean just
natural beauty or can we consider man-made objects? As for the word beauty,
do we want to limit our discussion to artistic beauty such as paintings and
sculptures, or should we consider poems and literature as well? Should we
discuss only natural beauty, such as stars and flowers, or should we consider
personal beauty as well, such as models and GRE instructors? As you can see,
we could write a lot on this topic, if we had the time. But we don’t, so it’s
important to focus. By defining our key terms, we make the essay a lot more
manageable and easier to write in a short amount of time. For this essay, let’s
include both natural objects and man-made artistic feats, but leave out
personal beauty.
Using key terms from the
prompt throughout your
essay contributes to its
overall coherency.
Opposite Side
In order to score well on the Issue essay, you’ll have to consider both sides of
the prompt. A simple “I agree, and here’s why” essay won’t be enough here;
rather, you’ll need to consider both sides of the issue and state a clear position
that you can defend. Take a brief moment to look at the sample prompt again,
and then write down the converse of the statement.
“True beauty is found not in the exceptional but in the commonplace.”
For this prompt, the opposite side of the argument would be something along
the lines of “True beauty is found not in the commonplace, but in the
exceptional.” Note that there is no right answer to the prompt; either side is
valid. So if you find the opposite of the statement more convincing, that’s
fine. As long as you can support your position with some relevant examples,
it doesn’t matter what position you take on the prompt. This brings us to the
final part of step one—brainstorming examples.
Examples
In many ways, the examples will be the most important part of your essay.
Without strong, relevant examples you cannot expect to achieve a high score
on the Issue essay. As the instructions state, you should support your position
with examples drawn from your reading, experience, observation, and
academic studies. In general, the more specific your examples are, the better
your essay score. And examples from history, literature, or current events are
better than personal observations or experiences. Imagine that a friend asks
you to read her essay and give feedback. Which sentence would you respond
more favorably to?
“Few observers would doubt the awesome beauty of the ceiling of the Sistine
Chapel in Rome, a work of art produced by the great Renaissance artist
Michelangelo.”
“Few observers would doubt the awesome beauty of the various paintings
they see in museums, works of art produced by great artists.”
Both sentences essentially say the same thing and use practically the same
words. But you would probably respond more favorably to the first sentence
because it contains a specific example.
Take a moment to jot down some examples for the previous prompt. Make
sure you come up with examples for both the original statement and its
opposite.
Now take a moment to look over your examples. Are they specific? Are they
relevant to the topic? Do they support a position on the topic? The strength of
your examples will determine the strength of your argument. It’s hard to write
a convincing paper with weak examples. Here are some examples that might
work for our sample topic, both weaker and stronger:
Okay Example
paintings, artwork
buildings, churches
flowers, natural wonders
Better Example
Leonardo da Vinci’s Mona Lisa
Notre Dame Cathedral in Paris
Niagara Falls
Good examples are relevant to the topic and contain specific details.
In each case, the better example is the more specific, more detailed example.
Also note that we’ve avoided any personal examples. While you certainly
may feel that your boyfriend or girlfriend is the most beautiful person in the
world, that sort of personal example won’t be as effective as a more academic
or global example. Use personal examples only when specifically instructed
to by the prompt or as a last resort.
Avoid hypothetical
examples—the more
specific your example is,
the better.
STEP 2: ORGANIZE
Once you’ve identified the key terms, considered the opposite side of the
issue, and generated some examples, it’s time to organize your thoughts.
Basically, you’ll want to do the following:
1. Separate Your Examples. How many of your examples support
the pro side and how many support the con side? Divide your
examples up and see which side has more support.
2. Write Your Thesis Statement. After evaluating the strength of
your examples, decide what position you will take in your essay,
and then write your thesis. Your thesis is the main point that you
want your essay to express.
Let’s continue the process on the sample prompt.
Separate Your Examples
Do this before you decide on your thesis statement. Even though you might
have a strong preference for one position on the issue, you might notice that
the examples you brainstormed tend to support the other side of the issue.
Don’t expend more time trying to think of examples to support your
preconceptions; just write your essay supporting the other side! There is no
right or wrong response. All that matters is being able to write a strong,
coherent essay in a very limited time. Your personal views or beliefs are
unimportant to the ETS graders. If we continue with the examples we used
earlier, they would probably break down like this:
Pro
natural wonders
Con
Mona Lisa
Notre Dame
Based on some of the examples we’ve come up with, it looks like we’d be
better off supporting the idea that “True beauty is found not in the
commonplace, but in the exceptional.” While natural wonders like sunsets
and flowers are pretty commonplace, we’ve come up with a lot more
exceptional examples. And it looks like we could even argue that it is the
exceptional natural wonders, such as Niagara Falls, that are truly beautiful.
It doesn’t matter what
side of the issue you
take on the GRE.
Write Your Thesis Statement
Now comes the culmination of all of our work. What point do we want to
make about the topic? Write it down on a sheet of paper.
Our thesis should probably be something along the lines of this: “While
certain commonplace natural objects are examples of beauty, true beauty is
most often found in rare, exceptional cases.”
Now that we have figured out what we want to say, we can focus on proving
why we believe it. But remember: Only after working through these steps are
we truly ready to write!
Practice: Steps 1 and 2
Work through steps one and two on the following Issue essay prompts below.
PROMPT 1
“Government funding should never be used to support art that the majority of the population finds
distasteful or objectionable.”
Write an essay in which you take a position on the statement above. In developing and supporting
your position, you should consider whether the above statement is always true or whether there are
exceptions to it.
On your scratch paper, write the (1) Key Terms, (2) Opposite Side, (3)
Examples, and (4) Thesis.
PROMPT 2
“Oftentimes, the results of a particular action are not of consequence; rather, it is the way we go
about the action that matters most.”
Write an essay in which you take a position on the statement above. In developing and supporting
your position, you should consider situations in which the ways matter most as well as situations in
which the results matter most.
On your scratch paper, write the (1) Key Terms, (2) Opposite Side, (3)
Examples, and (4) Thesis.
Practice: Sample Responses
Obviously, your examples and thesis statements will differ from those given
below, but these sample responses will give you a good indication of what to
aim for in your actual essay.
Prompt 1
Key Terms: What does support mean? Is that just giving money to the artist,
or does the government have to commission the work or promote it? What
population are we using to judge—the general population, the population of
artists, or some other population? What do we mean when we say art is
“objectionable” or “distasteful?” What standards are we using to determine
that?
Opposite Side: “Government funding should be used to support art, even if
the majority of the population finds the art distasteful.”
Examples: Robert Mapplethorpe controversy; National Endowment for the
Arts; Supreme Court rulings on obscenity; Government censorship
Thesis: “While artists have the right to create whatever objectionable art they
wish, taxpayers should not have to pay for art they find offensive or obscene.”
Prompt 2
Key Terms: What do we mean by consequence? Does this term refer to the
results of the action, or the effects the action has on the person doing the
action? Similarly, when we say the way we go about something “matters
most,” what criteria are we using?
Opposite Side: “The way we go about a certain action is not of consequence;
the results we get are what matter most.”
Examples: Rosa Parks, whose actions helped further the Civil Rights
movement; Gandhi, whose methods of nonviolent resistance played a part in
Indian independence; Revolutionary War, whose violent methods eventually
led to independence for the United States
Thesis: “While people do note the ways in which people go about certain
actions, it is usually the ultimate result that matters.”
STEP 3: WRITE
Now that we know how to prepare for our Issue essay, we can write it. In this
section, we’ll discuss various templates for essays and show you how you can
pre-construct certain portions of your essay. Before we do that, though, let’s
revisit your goals for the essay.
Essay Essentials Review
Remember the format of your essay should be
•
introduction
•
body paragraphs
•
conclusion
Another way to think about this structure is
•
Say what you’re going to say.
•
Say it.
•
Say what you said.
Preconstruction: The Introduction
For the Issue essay, a good introduction accomplishes the following tasks:
1. clearly establishes the topic of the paper
2. previews both sides of the issue at hand
3. presents a clear thesis
Let’s look at each of these tasks in detail and discuss different ways to
accomplish the goals of the introductory paragraph.
Establish the Topic
You want to make it clear what issue the essay is going to talk about. Even
though the grader will see the prompt you’re writing about, he or she should
be able to figure out the prompt just from reading the introduction of your
essay. There are a few different ways you can quickly establish the topic, so
let’s return to our original prompt and preconstruct some approaches.
Don’t just restate the
prompt! Come up with
a strong “hook” for the
beginning of your essay.
Here, once again, is our prompt:
“True beauty is found not in the exceptional but in the commonplace.”
Write an essay in which you take a position on the statement above. In developing and supporting
your essay, consider instances in which the statement does and does not hold true.
One of the worst ways of establishing the topic is to merely quote the prompt,
as that shows a lack of creativity and a potential lack of understanding of the
prompt itself. So let’s discuss some other ways to start our essay.
Approach 1: Rhetorical Questions
This approach is a tried-and-true way of introducing your topic. Instead of
simply quoting or paraphrasing the prompt, turn it into a rhetorical question.
Here are a few samples:
Where does true beauty lie, in the exceptional or in the commonplace?
Do we find the exceptional more beautiful or the commonplace?
Can we find beauty only in rare, exceptional instances or does it truly lie all
around us?
It is immediately clear what topic the essay will explore, from each of these
examples of introductory sentences. See if you can come up with a rhetorical
question for either this topic or one from the previous drill.
Approach 2: Famous Quotations
Another classic approach to beginning an essay is to use either a well-known
saying or a famous quote from someone. Many of the GRE topics are fairly
bland, so even if you can’t think of a famous quote, there are usually some
classic aphorisms you use. Here’s what we mean:
“Beauty is Truth, Truth Beauty,” or so said the romantic poet John Keats.
A common saying is that beauty is in the eye of the beholder.
Obviously, this type of introduction can be tough to do if something doesn’t
pop into your head right away. Try to come up with a quote or common
saying for this topic or one from the drill.
Approach 3: Anecdote
An anecdote is a brief story. Oftentimes you can grab your reader’s attention
and introduce the topic with a good anecdote. Consider this example:
It is said that Cézanne, the famed French painter, was so concerned with the
beauty of his paintings that he would destroy any of his works that he felt was
flawed.
The Romantic poet John Keats was so struck by the beauty of Chapman’s
translation of Homer’s work that he wrote a poem about it.
When using an anecdote you might have to write a sentence or two explaining
the relevance of your story. Try out an anecdote for this topic or one of the
drill topics.
A good opening line is
great to have, but if you’re
stuck, don’t spend an
excessive amount of time
trying to come up with
something clever.
Approach 4: Fact/Statistic
For some topics, it might be appropriate to start your essay by stating a fact or
statistic. Factual mistakes won’t cost you any points, because this is an essay,
not a book report. So don’t be afraid if your fact isn’t 100 percent accurate.
Here’s an illustration:
A recent scientific study showed that the faces that people find the most
beautiful are those that are the most symmetrical.
Psychologists have demonstrated that people’s responses to certain
phenomena are based on certain innate mechanisms in the brain.
Give this approach a shot, using this topic or one from the drill.
Approach 5: Definition
One way you may wish to start your essay is by defining one of the key terms
from the prompt:
Beauty, by definition, is that which moves us or impacts us significantly.
The “exceptional” typically refers to those things that stand out, which is also
a plausible definition for beauty.
The advantage to this approach is that you already spent some time thinking
along these lines when you were planning your essay. Come up with a sample
introductory sentence for this topic or one of the drill topics.
Preview the Issue
Once you’ve told the reader what the topic is, your next task is to inform the
reader of the issues at hand. You want to briefly touch on both sides of the
debate, explaining the pros and cons of the prompt. A good way to
accomplish this is to make use of strong transition words—words like but,
despite, while, and although. Here are some examples.
While some people can find beauty in the most common of places, true beauty
is found only in the exceptional.
Some would argue that beauty is found everywhere, from the flowers to the
stars, but others would state that true beauty is found only in rare, special
instances.
Despite the assertions of many that beauty is everywhere, true beauty is found
only in exceptional cases.
Although one might argue that many commonplace things are beautiful, it is
the exceptional things that possess true beauty.
There can be no doubt that some of the world’s most common things are
beautiful. And yet, it is often the exceptional objects that possess true beauty.
Practice writing sentences that address both sides of the issue. Use the sample
topic or one from the drill.
Present the Thesis
Your final task in the introduction is to present the thesis. Some writers prefer
to avoid the first person, refusing to use sentences such as “I believe…” or “I
feel…” However, there is no penalty for use of the first person. A more
important consideration when writing your thesis is giving some indication of
why you hold your particular position. You should make it clear that you’ve
thought about and analyzed the issue. Here are some examples of thesis
statements.
A good thesis tells the
reader exactly what your
position is and why.
I believe that beauty is truly found in the exceptional, not in the
commonplace, because if common things were beautiful, the very word would
lose its meaning.
In my view, beauty is found in the exceptional, not in the commonplace,
because only exceptional things really stand out as special in our minds.
It is clear that true beauty is not to be found in the commonplace but in the
exceptional. On closer inspection, even so-called common objects that people
consider beautiful are actually exceptional.
After weighing the evidence, it is certain that beauty is the province of the
exceptional, not the commonplace. People find true beauty in things that they
rarely experience, not the things they experience every day.
For each thesis, you can see that the author is also giving some justification
for the viewpoint. This justification will be of course explored more
thoroughly in the body paragraphs, but it’s good to give a preview of how
your essay will take shape. Try writing thesis statements for some of the
sample prompts.
Preconstruction: Body Paragraphs
A body paragraph should do the following:
1. use a good transition/topic sentence
2. present an example
3. explain how the example supports the thesis
Body paragraphs are a little harder to preconstruct because they are the most
specific part of the essay. Still, there are some handy tips for creating body
paragraphs that will make for a strong essay.
Transition/Topic Sentence
One attribute of the strongest essays is that they flow well. The best way to
write an essay like this is to use strong topic sentences and good transitions
for each of your body paragraphs. Your topic sentence should serve as a
gentle reminder of what the thesis of the essay is. Here’s an example:
One example of beauty found in the exceptional is Leonardo da Vinci’s Mona
Lisa.
A second instance in which true beauty lies not in the commonplace but in the
exceptional is Notre Dame Cathedral in Paris.
Of course, you might want to avoid using simple transitions like “the first
example,” and “the second example.” You can make your writing stronger by
leading with the example and making the transition a little more subtle, like
so:
Leonardo da Vinci’s Mona Lisa is surely one of the most exceptional, and
beautiful, paintings ever created.
Consider the beauty of Notre Dame Cathedral in Paris, a building that is in
no way commonplace.
Or to get even fancier, refer to the previous example in your transition
sentence:
Like da Vinci’s Mona Lisa, the cathedral of Notre Dame in Paris is an
exceptional, and exceptionally beautiful, object.
The important point is that each sentence introduces the example and reminds
the reader of the purpose of the example, which in this case is to support the
notion of beauty as exceptional. In the next few sentences, you’ll provide
details about your example. It’s important that you remember to link the
example to your thesis.
Explain How Your Example Supports Your
Thesis
On the GRE essays, don’t get so caught up in providing details for your
example that you forget to explain how or why your example helps your
thesis. The purpose of the Issue essay is not to just list some examples; the
purpose is to develop and support a position on the issue. Here’s an example
of a body paragraph that doesn’t quite fulfill that goal:
Don’t just state the
example; explain why the
example is relevant to your
thesis.
Like da Vinci’s Mona Lisa, the cathedral of Notre Dame in Paris is an
exceptional, and exceptionally beautiful, object. Notre Dame is a stunning
example of gothic architecture, famous for the flying buttresses that adorn the
sides of the building. The cathedral also has rows and rows of beautiful
sculptures recessed into the walls, as well as a gorgeous central stained-glass
window. These features make Notre Dame one of the most beautiful
cathedrals in the world.
The writer here did a good job of providing specific details about the
example, which definitely strengthens this paragraph. However, the writer
failed to explain why Notre Dame supports the view that true beauty is
exceptional, not commonplace. Let’s fix that:
Like da Vinci’s Mona Lisa, the cathedral of Notre Dame in Paris is an
exceptional, and exceptionally beautiful, object. Churches and cathedrals line
the streets of most major cities in Western Europe, but few possess the renown
of Notre Dame. Notre Dame is a stunning example of gothic architecture,
famous for the flying buttresses that adorn the sides of the building. The
cathedral also has rows and rows of beautiful sculptures recessed into the
walls, as well as a gorgeous central stained-glass window. These features
make Notre Dame one of the most beautiful cathedrals in the world.
Compared to a common church or cathedral, Notre Dame is truly aweinspiring; Victor Hugo used the building as the backdrop for his magnificent
book The Hunchback of Notre Dame and thousands of tourists travel untold
miles to view the cathedral. That sort of beauty is not possessed by just any
church on the corner.
This is a stronger body paragraph because it is more explicit in its discussion
of the thesis. The author notes that churches and cathedrals are fairly
common, but then argues that Notre Dame stands out as an exceptional
cathedral. The author concludes the paragraph by showing how Notre Dame
is more beautiful than any typical church. Just as the topic of the essay should
be clear from the introduction, the thesis should be clear from each body
paragraph.
Write a body paragraph for one of the examples for this sample topic, or one
of your examples from the practice. Make sure you have a good
topic/transition sentence, specific details for the example, and an explanation
of how or why the example is relevant to the thesis.
Preconstruction: Conclusion Paragraphs
Your essay should always have a conclusion, for two reasons. First, a
conclusion paragraph is evidence of good organization. It shows that you
knew exactly what points you wanted to make, you made them, and now
you’re ending the essay. And second, an essay that lacks a conclusion seems
incomplete, almost as if your writing abruptly ends before it should. This can
give a negative impression of your essay. Fortunately, conclusion paragraphs
are easy to write. A good conclusion:
1. alerts the reader that the essay is ending
2. summarizes the main points of the essay
Some test takers even prefer to write their introduction and conclusion first
and then fill in the body paragraphs. This strategy has the advantage of
making your essay seem complete even if you happen to run out of time
writing the body paragraphs.
Make sure your essay
has a conclusion.
Alert the Reader
Conclusion paragraphs have their own topic/transition sentences, which
generally should contain a word or phrase that signifies the end of the essay.
Here are some examples:
In conclusion, it’s clear that true beauty is found not in the commonplace, but
in the exceptional.
Ultimately, beauty lies in the exceptional, not in the commonplace.
As the bulk of the evidence shows, the exceptional, not the commonplace,
possesses true beauty.
Clearly, true beauty is found in exceptional things, not in commonplace ones.
The examples above all support the idea that we find true beauty in
exceptional cases, not in commonplace ones.
Write some conclusion sentences for this topic or a sample topic from the
sample prompts.
Summarize Main Points
Your conclusion should also summarize the main points of the essay, meaning
that it should mention the thesis and how the examples support it.
Additionally, you can briefly consider the implications of the thesis. Here are
some sample conclusions:
In conclusion, it’s clear that true beauty is found not in the commonplace, but
in the exceptional. The Mona Lisa and Notre Dame Cathedral are both
exceptional examples of fairly commonplace things and it is these exceptions
that are noted as truly beautiful. If anything, the commonplace serves only as
a contrast to what true beauty really is.
Ultimately, beauty lies in the exceptional, not the commonplace. While
paintings and churches are fairly commonplace, only a small few of them,
such as the Mona Lisa or Notre Dame, truly reach the heights of beauty. It is
in these exceptions that we find real beauty.
The examples above all support the idea that we find true beauty in
exceptional cases, not in commonplace ones. Common things may seem at
first glance to be beautiful, but once we compare these commonplace
examples to the truly exceptional ones, we see that the exceptional ones are
truly beautiful.
Try your hand at constructing a conclusion paragraph, once again using this
topic or one from the sample prompts.
Putting It All Together
Read through this sample essay that’s based on the basic five-paragraph
model. Then you’ll have the chance to try writing a similar essay for a
different prompt.
“True beauty is found not in the exceptional but in the commonplace.”
Write an essay in which you take a position on the statement above. In developing and supporting
your essay, consider instances in which the statement does and does not hold true.
Beauty, by definition, is that which moves us or impacts us significantly. Some
would argue that beauty is found everywhere, from the flowers to the stars.
But others would state that true beauty is found only in rare, special
instances. After weighing the evidence, it is certain that beauty is the province
of the exceptional, not the commonplace. People are moved most by things
that they rarely experience, not the things they experience every day.
Those who would argue that true beauty is everywhere might point to the
beauty of a flower, or the starlit night. These experiences are certainly
common, but do they show that true beauty is commonplace? Flowers might
be considered beautiful, but how often does a person stop to look at or
appreciate every flower? Flowers are so common that in many cases, they are
ignored or viewed as nothing special. However, on those rare occasions—
exceptional occasions, one might say—when we want to commemorate an
event or express emotion, we notice the beauty of flowers. Thus, it is not the
commonplace flower that strikes us as beautiful, but the exceptional situations
themselves that move us to appreciate the flower.
Now consider the exceptional. Leonardo da Vinci’s Mona Lisa is surely one of
the most exceptional, and beautiful, paintings ever created. Few people who
view the painting are not moved by the sheer beauty of it, and the Mona Lisa
is instantly recognized as a masterpiece of art. And yet, there have been
literally millions of paintings produced in human history. Is every single one
of them beautiful? Does every one of those paintings have the impact that da
Vinci’s does? Of course not. In order to find beauty, we must separate the
exceptional cases from the common ones. True beauty is such because it
stands out from the masses of the average and pedestrian.
Like da Vinci’s Mona Lisa, the cathedral of Notre Dame in Paris is an
exceptional, and exceptionally beautiful, object. Churches and cathedrals line
the streets of most major cities in Western Europe, but few possess the renown
of Notre Dame, one of the most beautiful cathedrals in the world. Compared
to a common church or cathedral, Notre Dame is truly awe-inspiring; Victor
Hugo used the building as the backdrop for his magnificent book The
Hunchback of Notre Dame and thousands of tourists travel untold miles to
view the cathedral. That sort of beauty is not possessed by just any church on
the corner.
In conclusion, it’s clear that true beauty is found not in the commonplace, but
in the exceptional. The Mona Lisa and Notre Dame Cathedral are both
exceptional examples of fairly commonplace things and it is these exceptions
that are noted as truly beautiful. If anything, the commonplace serves only as
a contrast so that we can understand what true beauty really is.
Your Turn
Try writing a similar essay for the prompt that follows this paragraph. Make
sure you consider the opposing side of the argument. Devote a paragraph to
looking at an example for the other side of the issue, but make sure you
indicate that there is a flaw in the example or that the example is less than
convincing. Set a timer for 30 minutes to practice GRE time constraints.
“People most respect the powerful not when they exercise their power, but when they refrain from
exercising it.”
Write an essay in which you develop and support a position on the statement above. In writing your
essay, you should consider both when the statement may be true and when it may be false.
How to Score Your Essay
Now it’s time to put on your essay-scoring hat and prepare to grade your own
essay. If you’re lucky enough to have a friend who is also preparing for the
GRE, you could switch essays and grade each other’s like you used to do in
sixth grade. You’ll need to be objective during this process. Remember, the
only way to improve is to honestly assess your weaknesses and systematically
eliminate them.
Set a timer for two minutes. Read the essay carefully but quickly, so that you
do not exceed the two minutes on the timer.
Now ask yourself the following questions about the essay:
1. Overall, did it make sense?
2. Did you address the topic directly?
3. Did you address the topic thoroughly?
4. Did your introduction paragraph repeat the issue to establish the
topic of the essay?
5. Did you consider both sides of the issue?
6. Did your examples make sense?
7. Did you flesh out your examples with details?
8. Did you explain how your examples supported your thesis?
9. Did your essay have a strong concluding paragraph?
10. Was your essay well organized, using transitions and topic
sentences?
11. Did you use language that made the organization of the essay
obvious?
12. Did you use correct grammar, spelling, and language, for the most
part?
If you could answer “yes” to all or almost all of these questions,
congratulations! Your essay would probably receive a score in the 5–6 range.
If you continue to practice, and write an essay of similar quality on the real
Analysis of an Issue section of the real test, you should score very well.
If you answered “yes” to fewer than 10 of the questions, you have room for
improvement. Fortunately, you also know which areas you need to strengthen
as you continue to practice.
If you answered “yes” to fewer than six of the questions, your essay would
probably not score very well on a real GRE. An essay of this quality would
not help you in the admissions process and could raise some red flags in the
minds of the admissions people. You need to continue to practice, focusing on
the areas of weakness that you discovered during this scoring process.
Another Sample Response
Take a look at a high scoring response to the prompt you just practiced on.
Your essay might look different and that’s fine. This is just one of many ways
to successfully complete the Issue essay assignment.
“The powerful are most respected not when they exercise their power, but when they refrain from
exercising it.”
Write an essay in which you develop and support a position on the statement above. In writing your
essay, you should consider both when the statement may be true and when it may be false.
What aspect of power engenders the greatest respect? Some would argue that
power inspires respect only by its ability to change things or bring about
results. This camp respects the powerful only when they demonstrate their
power by raising a massive army or bestowing charity on the less fortunate.
Others believe that the true measure of power lies not in what it is used for,
but in how it is restrained. These people believe that people most respect the
powerful when they choose not to use their power, such as granting clemency
to a criminal on death row or allowing critics of the government to speak out.
However, even in these cases of restraint, it is clear that the exercise of power
is more respected because of what that restraint implies about government
power and control.
Consider first the respect people hold for the exercise of power. One of the
mightiest displays of power is the ability to protect and safeguard people and
property and this aspect of government is what many people respect. Indeed,
in Hobbes’s Leviathan, he argued that one of the reasons people sacrifice
themselves for the good of the state is to preserve the power of the state to
protect its members from outside attacks. And one of the stated goals of the
United States massive military buildup was so that other countries would
either “love us or fear us.” Thus, it is clear that people have respect for
displays of power. Similarly, the ability of the powerful to bestow gifts of
charity on the less fortunate is also well respected. The names of
philanthropists like Carnegie and Rockefeller are held in high esteem because
they used their power to help those less fortunate than themselves.
On the other hand, the ability to show restraint can also engender respect.
Recently, the governor of Illinois decided to commute the death sentences of
all the prisoners on death row. Such an act of clemency brought high praise
from human rights proponents around the world. Furthermore, the fact that
democratic governments allow dissent when they could in many cases censor
or squash unfavorable opinions also lends credence to the view that restraint
of power is what people respect. For example, the arbitrary arrest and
sentencing of political dissidents in Russia has brought much international
criticism of the Kremlin, while countries that support freedom of speech and
the press are widely respected in the world.
Ultimately, after considering both sides of the issue, it must be concluded that
the exercise of power is most respected. This is because even in cases of
restraint, the entity in power is still exercising its power. Granting clemency is
possible only because the state holds the power of life and death. Allowing
dissent is exceptional only because the government has the power to crush it.
Thus, it is not the restraint of power that people most respect, it is the exercise
of it.
FINAL THOUGHTS: WHAT TO DO WITH YOUR
TIME
Now that you know how to construct your essay, you have to practice writing
essays in a mere 30 minutes. Here’s a guideline for how to use your time.
•
Find key terms, state the opposite side, brainstorm examples: 5–7
minutes
•
Formulate a thesis: 2 minutes
•
Write the essay: 18–20 minutes
•
Proofread: 1–2 minutes
Notice that not a lot of time is allotted for proofreading. Remember that it’s
okay to have minor spelling and grammatical errors. Your time is better spent
making sure you consider both sides of the issue completely and write an
effective essay. For tons more practice, you can go to www.ets.org/gre for the
complete list of essay topics.
Your essay doesn’t have to
be perfect. Focus on the
big picture.
Summary
Follow the three simple steps to essay success: Think, Organize, Write.
One of the keys to high scoring essays is good examples. Make sure
your examples are relevant to the topic and as specific as possible.
Try to use examples drawn from your readings, current events,
literature, and history. Avoid personal examples.
Spice up your writing by employing an interesting “hook” to get your
readers’ attention. Consider using such hooks as rhetorical questions,
quotes, anecdotes, facts and statistics, and other attention-getting
devices.
A good GRE essay presents a smooth flow of ideas and examples.
Make sure you use transitions to help show the progression of ideas in
your essay.
Templates can be effective ways of organizing your essay, but don’t feel
restricted to them. Come up with your own template or modify the
existing templates as you see fit.
Chapter 17
The Argument Essay
The Argument essay of the GRE asks you to examine and critique the logic of
an argument. The arguments you will see in this chapter are similar to the
ones you worked with in Chapter 7, and you will need to use the same
approach to breaking these arguments down. This chapter will show you how
to organize and write an essay once you’ve found the premises, conclusion,
and assumptions of a GRE argument.
You’ll be able to use all the skills we’ve discussed for the Analysis of an Issue
essays on this type of essay as well, but in a slightly different way. Instead of
asking for your opinion on a topic, the Analysis of an Argument essay asks
you to critique someone else’s argument. Before we jump into setting up
templates and other preconstruction steps, let’s take a look at how Analytical
Writing arguments work.
THE PARTS OF AN ARGUMENT
As you read in Chapter 7 on Critical Reasoning, an argument, for GRE
purposes, is a short paragraph in which an author introduces a topic and uses
reasoning or factual evidence to back up his or her opinion about that topic.
The following statement is a really simplified example of an argument:
My car broke down yesterday, and I need a car to get to
work. Therefore, I should buy a new car.
The car argument above is composed of the following three parts:
•
the conclusion—the author’s opinion and recommendation for
action
•
the premises—the facts the author uses to back up his or her
opinion
•
the assumptions—unstated conditions that must be true in order
for the argument to make sense
In this argument, the author’s conclusion is “I should buy a new car.”
The premises the author uses to support this conclusion are that his car broke
down yesterday, and that he needs a car to get to work.
The premises must support the conclusion the way table legs support a
tabletop. The tabletop is the most obvious and useful part of a table—you see
more of it, and you can put things on it. But without the legs to hold it up, it’s
just a slab of wood on the floor. The same is true for the conclusion of an
argument. The conclusion is the part that gets all the attention, since it
recommends some course of action, but without the premises to support the
conclusion, the conclusion won’t hold up.
Conclusion Words
Certain words indicate a conclusion.
•
so
•
therefore
•
thus
•
hence
•
showed that
•
clearly
•
then
•
consequently
•
as a result
•
concluded that
When you see these words, you can be relatively sure that you’ve found the
conclusion of the argument.
Premise Words
Certain words indicate premises.
•
because
•
since
•
if
•
given that
•
in view of
•
in light of
•
assume
ASSUMPTIONS
An assumption is an unstated premise that supports the author’s conclusion.
It’s the connection between the stated premises and the conclusion. In the
example of the table, the assumption is that nails or glue hold the legs and the
tabletop together. Without the glue or nails, the table will fall apart. Without
the assumption, the argument will fall apart.
Sometimes the assumption is described as the gap between the facts that make
up the premises and the conclusion. They don’t always connect, so the
assumption is the gap between them.
Let’s take a look back at the car argument:
My car broke down yesterday, and I need a car to get to
work. Therefore, I should buy a new car.
The premises are that my car broke down yesterday and I need a car to get to
work. The conclusion is that I should buy a new car.
When you first read this argument, you may have had some questions. These
questions might have been along the lines of “Why can’t the author just rent a
car?” or “Why can’t the author just fix the car?”
As you read an argument, identifying the premises and conclusion, questions
may pop into your head. Those questions are pointing out the gap that leads to
the assumption. Here, the gap is between having a broken car and still
needing a car to get to work on the one side, and having to buy a new car on
the other side.
Therefore, the assumption must be as follows:
There is no other way to have a car.
There are all sorts of smaller assumptions here—that the car can’t be fixed,
that a car can’t be rented, that there’s no other car the author can borrow—but
those are all covered in the main assumption.
The assumption fills the gap between the premises and the conclusion, and, in
fact, functions as an unstated premise:
My car broke down yesterday, and I need a car to get to work. There is no
other way to have a car. Therefore, I should buy a new car.
Brainstorming for the Argument Essay consists primarily of coming up with a
list of assumptions.
Three Common Types of Arguments and Their
Assumptions
There are three types of arguments you are likely to see. They are Sampling,
Analogy, and Causal. Becoming familiar with these three types will help you
identify the assumptions in the argument more quickly when the clock is
ticking on the real test.
1. The Sampling Assumption
A sampling argument assumes that a small group is representative of a much
larger group to which it belongs. To attack a sampling argument, show that
one cannot assume that the opinions or experiences of the smaller group are
necessarily representative of the larger group.
2. The Analogy Assumption
An argument by analogy assumes that A = B or that what is true for one entity
will be true for another. To attack an argument by analogy, simply show that
the two groups or places or individuals are nothing like each other. What is
true for one does not have to be true of the other.
3. The Causal Assumption
A causal argument assumes that A causes B, or that if you remove the cause,
you will remove the effect. While there may be a strong correlation between
A and B, it does not always follow that it is a causal relationship or that A is
the cause of B. To attack a causal relationship, point out that there are other
possible causes for B and brainstorm some possible examples.
Well, Great, But Why Do I Care?
You should care about taking apart the argument, and finding the assumptions
in particular, because the key to writing a great Argument essay on the
Analytical Writing section is ripping apart the argument.
Think about it. The official instructions on the test ask you to “critique” the
author’s argument. However, if you claim that everything the author says
makes sense, you won’t be able to write an essay that’s more than a few
sentences long. This means that in order to write a great essay, you’ll need to
tear the author’s argument apart.
Danger: The most common mistake people make in writing the
Argument essay is expressing their own opinions. Don’t do this! The
Issue essay specifically asks you to give an opinion and then back it up.
The Argument essay wants a critique of someone else’s opinion, not
your own.
WRITING THE ARGUMENT ESSAY
Writing the Analysis of an Argument essay requires a series of steps.
Step 1:
Read the topic and identify the conclusion and the
premises.
Step 2:
Since they’re asking you to critique (that is, weaken) the
argument, concentrate on identifying its assumptions.
Look for gaps in the argument, weaknesses in the logic,
and new information in the conclusion that wasn’t
present in the premises. Brainstorm as many different
assumptions as you can think of. Write these out on your
scratch paper or on the computer screen.
Step 3:
Select three or four of the strongest assumptions around
which to build your essay.
Step 4:
Choose a template that allows you to attack the
assumptions in an organized way.
Step 5:
Write the essay, using all the tools and techniques that
you’ll be learning in this chapter.
Step 6:
Read over the essay and edit it.
You will have 30 minutes
to plan and compose a
response to the argument
topic, so make sure to
budget your time wisely.
KEYS TO A HIGH-SCORING ESSAY
In the Analysis of an Argument topic section, your job is to critique the
argument’s line of reasoning and the evidence supporting it, and to suggest
ways in which the argument could be strengthened. Again, you aren’t
required to know any more about the subject than would any normal person—
but you must be able to spot logical weaknesses. Make absolutely sure you
have read and understood the previous section about taking apart the
argument.
In order to write a high-scoring essay, you’ll want to accomplish four key
tasks. According to a booklet prepared by ETS, “An outstanding argument
essay…clearly identifies and insightfully analyzes important features of the
argument; develops ideas cogently, organizes them logically, and connects
them smoothly with clear transitions; effectively supports the main points of
the critique; and demonstrates superior control of language, including diction,
syntactic variety, and the conventions of standard written English. There may
be minor flaws.”
To put it more simply, your essay should demonstrate all of the same things
that you did for the Analysis of an Issue essay, plus one extra ingredient: a
cursory knowledge of the rules of logic.
Your opinion is not the
point in an Analysis of an
Argument essay.
Doing the Actual Analysis of the Argument
In any Analytical Writing argument, the first thing you should do is separate
the conclusion from the premises.
Let’s see how this works with an actual essay topic.
Topic:
The director of the International Health Foundation
recently released this announcement:
“A new medical test that allows the early detection of a
particular disease will prevent the deaths of people all
over the world who would otherwise die from the
disease. The test has been extremely effective in
allowing doctors to diagnose the disease six months to a
year before it would have been spotted by conventional
means. As soon as we can institute this test as routine
procedure in hospitals around the world, the death rate
from this disease will plummet.”
Save the fancy prose for
English class! Your grader
cares more that you can
identify the parts of the
argument than for a clever
turn of phrase.
The conclusion in this argument comes in the first line:
A new medical test that allows the early detection of a
particular disease will prevent the deaths of people all
over the world who would otherwise die from that
disease.
The premises are the evidence in support of this conclusion.
The test has been extremely effective in allowing
doctors to diagnose the disease six months to a year
before it would have been spotted by conventional
means.
The assumptions are the unspoken premises of the argument—without which
the argument would fall apart. Remember that assumptions are often causal,
analogical, or statistical. What are some assumptions of this argument? Let’s
brainstorm.
Brainstorming for Assumptions
You can often find assumptions by looking for a gap in the reasoning.
“Medical tests allow early detection”: According to the conclusion, this
medical test leads to the early detection of the disease. There doesn’t seem to
be a gap here.
Early detection allows patients to survive: In turn, the early detection of the
disease allows patients to survive the disease. Well, hold on a minute. Is this
necessarily true?
•
First, do we know that early detection will necessarily lead to
survival? We don’t even know if this disease is curable. Early
detection of an incurable disease is not going to help anyone
survive it.
•
Second, will the test be widely available and cheap enough for
general use? If the test is expensive or available only in certain
parts of the world, people will continue to die from the disease.
•
Third, will doctors and patients interpret the tests correctly? The
test may be fine, but if doctors misinterpret the results or if
patients ignore the need for treatment, then the test will not save
lives.
Death rate will plummet: There’s a huge gap here in that there’s absolutely no
explanation of how merely detecting the disease will immediately cause the
death rate from it to plummet. This area is ripe for exploration.
Organizing the Analysis of an Argument Essay
We’re now ready to put this into a ready-made template. In any Analysis of an
Argument essay, the template structure should be pretty straightforward:
You’re simply going to reiterate the argument, attack the argument in three
different ways (each in a separate paragraph), summarize what you’ve said,
and mention how the argument could be strengthened. From an organizational
standpoint, this is pretty easy. Try to minimize your use of the word I. Your
opinion is not the point in an Analysis of an Argument essay.
The arguments provided
for the writing assessment
of the GRE typically contain
more flaws than those
you worked with in the
multiple-choice section.
The flaws are often easier
to spot as well.
A Sample Template
Of course, you will want to develop your own template for the Analysis of an
Argument essay, but to get you started, here’s one possible structure:
The argument that (restatement of the conclusion) is not entirely
logically convincing, since it ignores certain crucial assumptions.
First, the argument assumes that:
Second, the argument never addresses:
Finally, the argument omits:
Thus, the argument is not completely sound. The evidence in
support of the conclusion is not sufficient to support the
conclusion of the argument because:
Ultimately, the argument might have been strengthened by:
The key to succeeding on an Analysis of an Argument essay is to critique the
argument clearly.
How Would the Result of Our Brainstorming
Fit into the Template?
Here’s how the assumptions we came up with for this argument would fit into
the template:
The argument that the new medical test will prevent deaths that
would have occurred in the past is not entirely logically
convincing since it ignores certain crucial assumptions.
First, the argument assumes that early detection of the disease
will lead to an immediate drop in the mortality rate from this
disease, yet it does nothing to explain how this will happen, and
so on.
Second, the argument never addresses the point that the
existence of this new test, even if totally effective, is not the
same as the widespread use of the test, and so on.
Finally, even supposing the ability of early detection to save lives
and the widespread use of the test, the argument still depends
on the doctors’ correct interpretation of the test and the patients’
willingness to undergo treatment, and so on.
Thus, the argument is not completely sound. The evidence in
support of the conclusion that the test will cause death rates to
plummet does little to prove that conclusion, since it does not
address the assumptions already raised. Ultimately, the
argument might have been strengthened if the author could have
shown that the disease responds to early treatment, which can
be enacted immediately upon receipt of the test results, that the
test will be widely available around the world, and that doctors
and patients will make proper use of the test.
Customizing Your Analysis of an Argument
Template
Your organizational structure may vary in some ways, but it will always
include the following elements: The first paragraph should sum up the
argument’s conclusion. The second, third, and fourth paragraphs will attack
the argument and the supporting evidence. The last paragraph should
summarize what you’ve said and state how the argument could be
strengthened. Here are some alternate ways of organizing your essay:
Variation 1
1st paragraph: Restate the argument.
2nd paragraph: Discuss the link (or lack thereof) between the conclusion
and the evidence presented in support of it.
3rd paragraph: Show three holes in the reasoning of the argument.
4th paragraph: Show how each of the three holes could be plugged up by
explicitly stating the missing assumptions.
5th paragraph: Summarize and conclude that because of these three holes,
the argument is weak.
Variation 2
1st paragraph: Restate the argument and say it has three flaws.
2nd paragraph: Point out a flaw and show how it could be plugged up by
explicitly stating the missing assumption.
3rd paragraph: Point out a second flaw and show how it could be plugged
up by explicitly stating the missing assumption.
4th paragraph: Point out a third flaw and show how it could be plugged up
by explicitly stating the missing assumption.
5th paragraph: Summarize and conclude that because of these three flaws,
the argument is weak.
Write Your Own Template for the Argument Topic
1st paragraph:
2nd paragraph:
3rd paragraph:
4th paragraph:
5th paragraph:
You Are Ready to Write an Argument Essay
You’ve separated the conclusion from the premises. You’ve brainstormed for
the gaps that weaken the argument. You’ve noted how the premises support
(or don’t support) the conclusion. Now it’s time to write your essay. Start
typing, indenting each of the four or five paragraphs. Use all the tools you’ve
learned in this chapter. Remember to keep an eye on the time. Again, if you
have a minute at the end, read over your essay and do any editing that’s
necessary.
What to Do with Your Time
Now that you know how to construct your essay, you have to practice writing
essays in a mere 30 minutes. Here’s a guideline for how to use your time.
•
Break down the argument: 3–4 minutes
•
Find 2–3 assumptions: 3–4 minutes
•
Write the essay: 18–20 minutes
•
Proofread: 1–2 minutes
As was the case with the Issue essay, not a lot of time is allotted for
proofreading. Remember that it’s okay to have minor spelling and
grammatical errors. Your time is better spent making sure you consider both
sides of the issue completely and write an effective essay.
Practice: Writing an Argument Essay
Practice on the following sample argument topic. If you have access to a
computer, turn it on and start up a word-processing program (again, you may
want to use a very rudimentary one like Notepad to simulate the ETS program
you’ll see on the real test). Then set a timer for 30 minutes. In that time, read
the topic, brainstorm in the space provided in this book, and then type your
essay into the computer.
A Sample Argument
The market for the luxury-goods industry is on the
decline. Recent reports show that a higher
unemployment rate, coupled with consumer fears, has
decreased the amount of money the average household
spends on both essential and nonessential items, but
especially on nonessential items. Since luxury goods
are, by nature, nonessential, this market will be the first
to decrease in the present economic climate, and luxury
retailers should refocus their attention to lower-priced
markets.
Conclusion:
Why? (premises)
Assumptions:
Ways you can pull the argument apart:
Ways the argument could be made more compelling:
Now use the template you developed earlier in this chapter to type your essay
on a computer.
When writing your essay,
make sure to use terms
like causal, analogy,
sampling, and so forth.
Nothing impresses an
ETS grader more than a
sentence like “The
argument assumes the
sample is representative.”
How to Score Your Essay
It’s time to put on your essay-scoring hat and prepare to grade your own
essay. (Again, if you’re lucky enough to have a friend who is also preparing
for the GRE, you could switch essays.) You’ll need to be objective about the
process. The only way to improve is to honestly assess your weaknesses and
systematically eliminate them.
Set a timer for two minutes. Read the essay carefully but quickly, so that you
do not exceed the two minutes on the timer.
Now ask yourself the following questions about the essay:
1. Overall, did it make sense?
2. Did you address the argument directly?
3. Did you critique the argument thoroughly?
4. Did your introduction paragraph repeat the argument to establish
the topic of the essay?
5. Did you avoid injecting your own opinion into the essay?
6. Did your essay have three strong paragraphs critiquing the
arguments?
7. Did your critiques make sense?
8. Did you flesh out your points to make the weaknesses of the
argument explicit?
9. Did the examples apply directly to the topic?
10. Did the essay have a strong conclusion paragraph?
11. Was the essay well organized?
12. Did you use language that made the organization of the essay
obvious?
13. Did you use correct grammar, spelling, and language, for the most
part?
14. Was the essay of an appropriate length (four to five paragraphs of
at least three sentences each)?
If you could answer “yes” to all or almost all of those questions,
congratulations! Your essay would probably receive a score in the 5–6 range.
If you continue to practice, and write an essay of similar quality on the
Analysis of an Argument essay on the real test, you should score very well.
If you answered “yes” to fewer than 12 of the questions, you have room for
improvement. Fortunately, you also know which areas you need to strengthen
as you continue to practice.
If you answered “yes” to fewer than five of the questions, your essay would
probably not score very well on a real GRE. You need to continue to practice,
focusing on the areas of weakness that you discovered during this scoring
process.
There are more Argument topics for you to practice in the back of this book,
but if you’d like to practice even more, go to www.ets.org/gre and view the
list of real Argument topics. You cannot possibly practice writing essays on
all of these real ETS topics, so don’t even try. However, you should spend
time reading through them to become familiar with the variety of topics that
ETS may give you.
Just Keep Practicing
So now you’ve read everything you need to know about writing high-scoring
essays on the GRE. With a little practice, writing these essays should become
second nature, and you’ll find yourself sitting at the word processor on test
day confident and prepared. Keep it up!
Summary
Always start by identifying the conclusion of the argument.
Look for the common types of arguments: Sampling, Analogy, and
Causal.
Brainstorm all of the assumptions that attach the premises to the
conclusion.
Outline your essay on your scratch paper before you start writing.
Leave yourself two minutes to proofread your essay once you are done
writing.
Part V
Answers and Explanations to Drills
and Practice Sets
CHAPTER 4: TEXT COMPLETIONS
Practice: Finding the Clue
1.
Your words: harrowing, difficult, troubled; Underline: reflected in the
harrowing nature…of his plays
2.
Your words: tall, high, towering; Underline: second highest mountain
in the world…reaching more than 28,000 feet high
3.
Your words: negative, harmful, unhealthy; Underline: wind-chill
warning is issued…minus 25 degrees Fahrenheit or lower
4.
Your words: remnants, remains, artifacts OR devices, munitions,
projectiles; Underline: unexploded shells…from World War II
5.
Your words: non-interchangeable, distinct, different; Underline: use
the terms interchangeably…mammoths were hairy with long tusks,
while mastodons had low-slung bodies and fatter skulls
6.
Your words: practical, pragmatic, apolitical; Underline: he crafted
his policies not with an eye toward their political consequences but
instead toward their practical effects
7.
Your words: amount, volume, workload; Underline: he would have to
read for hours and hours each day to finish it all
8.
Your words: derived, descended, transcribed; Underline: word
“ghoul”…from the Arabic word “Algol”
Practice: Clues and Transition Words
1.
Your words: bad, poor, uneven; Underline: top talents…performance
as a rookie almost ended his career; Circle: but
2.
Your words: praise, recognition, respect; Underline: she brokered a
diplomatic solution to a potential crisis; Circle: work; she
3.
Your words: beneficial, health-promoting, healthful; Underline:
detrimental to one’s health; Circle: While
4.
Your words: disconnected, apart, isolated; Underline: increasing
technological connectivity; Circle: Despite
5.
Your words: attractive, graceful, charming; Underline: ugliness and
clumsiness; Circle: Although
6.
Your words: gauge, predictor, sign; Underline: use holiday sales to
gauge future stock prices; Circle: prices; thus
7.
Your words: negativity, misgivings, doubts; Underline: it is somewhat
ironic…negative view; Circle: while…rarely display such
8.
Your words: (devastating) effects, harms, toxicity; Underline:
devastating effects on insects; Circle: insects; however…the same
Text Completions Drill
1.
B
sorrow
The blank is describing what her eyes relayed and the transition
word despite indicates that what her eyes relayed must be the
opposite the smile that spread from ear to ear. A good word for the
blank is something like “sadness.” Choice (A), jubilance, means
something joyous, so eliminate it. Choice (B), sorrow, is a good
match, so keep (B). Lively means energetic, so eliminate (C).
[V]ision offers no contrast to “sadness,” and mischievousness or
naughtiness is closer to smile than to “sadness,” so eliminate (D)
and (E). The correct answer is (B).
2.
D
acute
The blank is describing black bears…claws. The transition word
[w]hile indicates that the claws of black bears are different from
those of grizzly bears which are described as long, flat, and
somewhat blunt. Black bears’ claws are described in the sentence
as short and curved, which are the opposite of long and flat.
Therefore, a good word for the blank is the opposite of somewhat
blunt, so use “sharp” and evaluate the answer choices. Choice (A)
obtuse is a synonym for blunt, so eliminate (A). Choice (B),
abominable may describe a bear, but the word doesn’t mean
“sharp” and so doesn’t match the clue, eliminate (B). Choice (C),
barren, is not a match for “sharp” so eliminate it. Choice (D),
acute, is a good match for “sharp,” so keep (D). Choice (C), fearful
does not match “sharp,” so eliminate it. The correct answer is (D).
3.
C
static
The blank is describing individual personalities. The semicolon
indicates that the clause before the semicolon should agree with the
clause following it. Therefore, the duality of stability versus
change must be matched in the second clause by the duality
describing personalities—the word in the blank or different. The
adjective different in the second clause corresponds to change in
the first, so the word in the blank must be an adjective
corresponding to stability. Recycle from the clue and use “stable.”
Choice (A) transient, means last for a short period of time, so
eliminate (A). Choice (B), maladjusted is not a match for “stable”
so eliminate it. Choice (C), static, is a good match for the “stable”
so keep (C). Choice (D), disturbed, and (E), discreet, are both not
poor matches for “stable,” so eliminate (D) and (E). The correct
answer is (C).
4.
E
prodigious
The blank is describing the kind of economic ripples caused by
[t]he Erie Canal’s completion. The clause after the semi-colon
provides further insight into the sentence: property values and
industrial output…rose exponentially. Therefore, these ripples
could thus be described as significant or “large,” so use this word
for the blank. Choice (A), persistent, is not a match for “large” so
eliminate it. Choice (B), invaluable doesn’t quite mean “large,”
and (C), incredulous, is nothing like “large” so eliminate (B) and
(C). [S]evere might describe a significant economic effect, but that
effect would be negative, not positive as implied here, so eliminate
(D). Choice (E), prodigious, meaning impressively great or large,
is a good match for “large.” The correct answer is (E).
5.
B
stolidity
The blank is describing how voters…respond to the levy of a new
tax. The clue in the sentence is the word inured, which means
hardened to a negative situation. If [v]oters are inured, then their
response to the levy of a new tax would not be strong. Thus the
word in the blank could be “resignation.” Choice (A), amazement,
is not a match for “resignation” so eliminate (A). Choice (B),
stolidity, or lack of emotion, is a good match so keep (B). Choice
(C), exasperation, may describe how voters feel generally towards
politicians, but is not supported by the passage so eliminate (C).
Choice (D), alarm, and (E), perplexity, are both poor matches for
“resignation,” so eliminate both answer choices. The correct
answer is (B).
6.
B
commensurate
The blank is describing when…it is desirable to expand the yield of
a harvest. The sentence provides further insight into this by stating
that it is desirable to expand…yield, but only if there aren’t also
certain additions in time, exertion and other variable factors of
production. So, a word such as “similar” for the blank conveys the
logic that expanded yield shouldn’t require expanded additions in
time and other factors. Choice (A), predestined, is not a match for
“similar” so eliminate (A). Choice (B), commensurate, is a good
match for the blank so keep (B). Choice (C), deliberate, is not a
match for the blank, so eliminate it. Choice (D), analogous is
close, but commensurate is more quantitative, so eliminate (D).
While indeterminate or uncertain additions are certainly not
desired, this choice doesn’t match “similar,” so eliminate (E). The
correct answer is (B).
Text Completions Practice Set
1.
B
futile
The clue is “global interconnectedness on the rise.” In such a
situation, the United States might allow its own interests to be
harmed if it tried to stay neutral during wartime. Thus, you need a
word that means doomed for the blank. Something presumptuous is
not necessarily doomed, while pragmatic and admirable take the
sentence in the wrong direction. Contemptuous, in contrast, makes
no sense in the blank’s context. Futile is the best choice.
2.
B
enamored of
Choose carefully here. The clue is “the dancers alone made his trip
worthwhile.” Thus, Flaubert was impressed by them. Enamored of
is the only choice that captures such a feeling. Overwhelmed by is
extreme, and implies that Flaubert got into more than he could
handle. Taken aback by, in contrast, merely suggests that our
traveler was surprised by the dancers; we cannot be sure that his
surprise was pleasant. Meanwhile, beseeched by does not indicate
how Flaubert felt, whereas if he were flustered by the performers,
he would not likely have found his encounter with them
worthwhile.
3.
A
fragile and E vulnerability
Try working with the second blank first. The clue is “facade of
calm that covers our anxiety.” The transition and tells you that you
are going in the same direction. Therefore, the word in the second
blank should be something similar to anxiety. Vulnerability is the
best fit. Nothing in the sentence supports a word as strong as
terror, and humor goes in the wrong direction. For the first blank,
if our facade is “flimsy and effortlessly ruptured,” it is likely that
the human race is delicate. Fragile is the only choice that matches.
4.
B
prerogative and F attainable by
Try working with the second blank first. The clue is “…when the
increased popularity of dime novels, the expansion in the number
of bookstores, and the introduction of the paperback made
books….” Therefore, find a word for the second blank similar to
accessible. Attainable by is the best choice. The first blank
describes the situation before books became accessible, so buying
them would have been a privilege limited to the well-to-do.
Prerogative is the best choice.
5.
A
an ineluctable and F merely denouement
If district boundaries are designed to protect incumbents—that is,
those already in office—then victory for those incumbents should
be close to assured or inevitable. Ineluctable is synonymous with
these words. Invidious means “causing envy” and plangent means
“full of lamentation,” neither of which is as well supported as the
credited response. The second blank comes after a couple of
transition words. The first is Of course, which might sound like the
passage is continuing in the same direction, but here indicates a
change of direction: The author is conceding that sometimes
incumbents face challenges. The second, Nevertheless, also
changes direction, meaning that the passage has returned to where
it started, arguing that elections are essentially decided before they
begin. That is what merely denouement means. Seldom nugatory
means rarely inconsequential, which is the opposite of what the
passage calls for; remarkably contentious is wrong for the same
reason, as that phrase would indicate that the general election is
fiercely contested.
6.
A
pedantic and D antediluvian
The first blank describes a group of professors. The clue is that
these professors “continue to insist that video games will never be
a proper object of study.” The transition While also means that
these professors are different from the rising generation of more
heterodox academics. So, a good word for the first blank is
something like orthodox. Of the answers, only pedantic, which
means overly concerned with the formalisms of teaching, comes
close to meaning orthodox. The second blank describes how the
rising generation regards the talk of the first group of professors.
Since the rising generation is more heterodox, they would likely
regard the view of the more orthodox professors as outdated. The
word antediluvian—literally, before the flood—means extremely
old-fashioned. Pusillanimous means cowardly, and jejune means
vapid and immature, so eliminate these choices.
7.
C
fulfilled, F changes, and H perilously
Try working with the first blank first. The clue for the first blank is
“predictions generally…accurate.” The transition however tells you
that the first and second parts of the sentence are in contrast to each
other. Predictions are usually right, the first part of the sentence is
saying, when things go as normal. Put something like true in the
first blank. Fulfilled fits nicely. The second and third blank must be
filled together in order to complete the second sentence. The
transition however shows that the second sentence changes
direction. You would expect predictions to be wrong when there
are changes, which is a choice for the second blank. Substantial
changes would make predictions very wrong, so perilously is the
best choice.
8.
B
dense, F liquid, and G an illustration
The clue for the first blank is the “floating” ice. So, ice is less
heavy than water. Only dense fits. There is nothing to support that
water is more intriguing than ice. All solids are less aqueous than
liquids. For the second blank, the transition than tells you to
change direction from solid. Another clue is water compared to ice.
Only liquid fits. For the third blank, the clue “the floating ice in
your water” is offered as an example. Only an illustration fits.
9.
C
practicing, E articulate, and I unfamiliar
For the first blank, Molly could comprehend Spanish before their
trip, so she was becoming familiar with Spanish. Only practicing
fits. Mastering goes too far. Now you can turn your attention to the
third blank. Because she is learning Spanish, it must be a new
language for her, and only unfamiliar fits for the third blank. For
the second blank, the transition although tells you to change
direction from the clue comprehend. She could not state her
thoughts. Only articulate means “state.”
10.
B
demarcates, D apocryphal, and I senescence
The first blank refers to what some people believe about the human
lifespan representing the outer bounds of animal longevity in
relation to that of other animals. So, look for a word that means
marker. Demarcates is the best fit, as belies means contradicts, and
antedates means comes before. The second blank refers to the
stories of musket balls being found in turtle shells and how some
people tend to dismiss tales about turtles living a long time, so a
word such as questionable would fit. Apocryphal means
questionable, making it the best choice. The clue for the final blank
is that some turtles show(ing) no signs of aging even as they pass
the two-century mark so look for a word that works with negligible
to create a phrase that means “not growing old.” Senescence means
growing old and when combined with negligible, is a good fit for
this clue.
CHAPTER 5: SENTENCE EQUIVALENCE
Sentence Equivalence Drill
1.
C
modern and E contemporary
The blank is describing the observer. The sentence gives further
insight into the blank with the word ancient and the transition word
or which indicates that a good word for the blank is the opposite of
ancient. Therefore, a good word for the blank could be “modern.”
Choice (A), antiquated, is the opposite of “modern” so eliminate
(A). Choice (B), perceptive, is a poor match for “modern,” so
eliminate it. Choice (C), modern, is a perfect match, so keep (C).
Choice (D), astute, is not a match for “modern,” so eliminate it.
Choice (E), contemporary, is a good match, so keep it. Choice (F),
archaic, is the opposite of “modern,” so eliminate it. The correct
answer is (C) and (E).
2.
D
innate and F inborn
The blank is describing characteristics. The passage gives further
insight by stating that some arise through experience and that
[r]esearchers are interested in the nature versus nurture debate.
This duality is reflected later in the sentence when it’s explained
why these researchers use identical twins…separated at birth to
explore this debate. Characteristics which arise through experience
correspond to nurture, so the characteristics described by the blank
should correspond to nature, so use “natural” as the word for the
blank. Intractable is a poor match for “natural” so eliminate (A).
Choice (B), nascent, means just coming into existence, which
sounds like it could match “natural” but does not fit because
something does not have to be “natural” to be called nascent.
Eliminate (B). Choice (C), erudite, means scholarly, so eliminate it.
Choice (D) is a good match for the blank, so keep it. Choice (E),
predilection, means a preference, so eliminate it. Choice (F) is a
good match for the blank, so keep it. The correct answer is (D) and
(F).
3.
A
capricious and D unconventional
The blank is describing the behavior and the sentence gives further
insight into the clue by stating that the Canadian Prime Minister is
eccentric. So, a good word for the blank is “eccentric.” Choice (A),
capricious, is a good match for “eccentric,” so keep (A). Choice
(B), lackluster, means not to standard, so eliminate it. Choice (C),
poised, is the opposite of “eccentric” so eliminate (C). Choice (D),
unconventional, is a good match for the blank, so keep (D). Choice
(E), repulsive, could describe behavior in some, but is not a match
for “eccentric” so eliminate (E). Choice (F), decorous, is also the
opposite of “eccentric” so eliminate (F). The correct answer is (A)
and (D).
4.
B
dynamic and F oscillating
The blank is describing the conditions of life. The sentence gives
further insight into the blank by listing examples of what the
conditions of life could be, such as…atmospheric pressure,…
physical activity, and diet. This clues imply that the conditions of
life are “varying.” Choice (A), inveterate, means have a longstanding habit, so eliminate it. Choice (B) is a good match for the
blank, so keep it. Choice (C), timorous, means nervousness, so
eliminate it. Choice (D), cowed, means to pressure by intimidation,
so eliminate it. Choice (E), turgid, means swollen, so eliminate (E).
Choice (F) is a good match for the blank, so keep it. The correct
answer is (B) and (F).
5.
B
commandeer and F appropriate
The blank is describing what the armed forces did to any working
form of transportation they could find. The sentence gives further
insight into the blank by stating the armed forces were without an
adequate number of vehicles of their own, after arriving…days
after Hurricane Zelda. So, the armed forces were “taking over”
any form of transportation. Choice (A), repatriate, means to send
someone back to their home country, so eliminate (A). Choice (B),
commandeer, is a good match, so keep it. Choice (C), extradite,
means to hand over someone to a judicial system, so eliminate (C).
Choice (D), interdict, means to prohibit, so eliminate (D). Choice
(E), expurgate, means to remove something questionable, so
eliminate (E). Choice (F), appropriate, is a good match for the
blank, so keep (F). The correct answer is (B) and (F).
Sentence Equivalence Practice Set
1.
B
affinity and F predilection
The word in the blank is used to describe Jim’s feelings for
gumdrops. The clues “enjoyed all kinds of candy” and “his
absolute favorite” indicates that the blank means liking. Both
affinity and predilection mean liking. Odium and disregard go in
the wrong direction. Container might sound right, but it is not
related to the clue. Nature does not mean liking.
2.
A
fiasco and B debacle
The blank concerns the Wright brothers’ first attempt at flying. The
clue is that their “subsequent efforts similarly ended in failure.”
Recycle the clue, and put failure in the blank. Fiasco and debacle
are the best matches. Triumph and feat have the opposite meaning.
Hindrance is not close enough, and precedent does not mean
failure.
3.
D
diminishes and F wanes
The clue “due to the increased aerodynamic drag” suggests that
fuel efficiency is likely to decrease as speed increases. Diminishes
and wanes both mean decreases. Eliminate equalizes and stabilizes
because they mean the fuel efficiency evens out. Adapts and
increases do not fit the clue, and neither has a synonym among the
other answer choices.
4.
B
an inept and F a maladroit
Despite acts as a change-of-direction transition that, combined with
“vast amount of time Francis dedicated to learning six different
languages,” tells you that something is wrong with Francis’s
communication skills. The last part of the sentence provides an
additional clue: “failed to redress his inability to construct cogent
prose” means that he doesn’t make sense. The blank must mean
ineffective, so inept and maladroit are the correct answers. Nothing
tells us how Francis feels, so morose won’t work. Astute is the
opposite of what’s needed. Though it’s possible Francis is florid
and prolific, the clues don’t directly support these ideas.
5.
E
temperament and F humor
The main clues are that one twin is described as sanguine, the other
choleric; even if you don’t know these words, the phrases “even in
times of stress” and “angry outbursts” suggest that they are words
used to describe personality. Temperament is a good synonym for
personality. While it is frequently used to mean comedy, humor
can also mean personality, especially in conjunction with words
such as sanguine and choleric, which derive from the ancient belief
that temperament was shaped by the levels of different fluids, or
humors, in a person’s body. The remaining choices don’t fit:
Environment means one’s surroundings, while the other three
words are concerned with the physical rather than the mental.
CHAPTER 6: READING COMPREHENSION
Reading Comprehension Drill
1.
A
The passage contains a mixture of information about the aye-aye,
both from a scientific and cultural background. It gives an
overview of the animal without giving a lot of detail in any one
area. Choice (B) is incorrect because the passage mentions
evolution only briefly, at the very end. This choice is too narrow.
Choice (C) is incorrect because the style of the passage is too
advanced for young students. Choice (D) is incorrect because the
passage mentions religion only as it relates to the fate of the ayeaye. Choice (E) is incorrect because the information given is
focused more on the aye-aye itself than on the culture of
Madagascar.
2.
A
The author refers to the aye-aye as a “superb example of life’s
variety.” Because this is a positive statement, look for a positive
answer. Choice (D) is negative. Choice (E) means sad. Choice (B)
means confused. Choice (C) is positive but is too extreme.
Therefore, (A), admiring, is the correct answer.
3.
“The aye-aye has been listed as an
endangered species and, as a result, the government of
Madagascar has designated an island off the northeastern coast
of Madagascar as a protected reserve for aye-ayes and other
wildlife.”
The author draws the conclusion that the aye-aye may become
extinct because the animals are killed on sight and their habitat is
being cut down. If some of the animals are in a protected reserve,
then not all of them will be affected by the circumstances cited by
the author.
4.
A
and B
Choices (A) and (B) can both be inferred from the passage. Choice
(A) is supported by the first paragraph. The classification of the
aye-aye changed, which demonstrates that such classifications are
not absolute. Choice (B) is supported by the part of the passage
dealing with the future of the aye-aye. It states that the aye-aye is
seen as an omen of death in the traditional religion of Madagascar.
Augury refers to the use of omens, so this statement must be true.
Choice (C), however, is not supported. Although the passage states
that the aye-aye is in danger, it does not directly discuss whether
this is due to limited resources on the main island.
5.
A
In the passage, the critics argue that for a piece of literature to be
great, it must be hard for the average reader to understand. Choice
(A) depicts an analogous situation of avant-garde movies deemed
superior to Hollywood blockbusters simply because their storylines
are more complicated and presumably harder to understand.
6.
E
The passage states, “rather than the to-be-expected socialist
harangue, Allende subtly works her political message within the
fabric of the compelling narrative she weaves.” In other words, a
reader might have expected Allende to include strong socialist
propaganda within her novel, but she did not. Choice (A) is
incorrect. Although the passage talks about Allende’s background,
it is not clear that her novel is autobiographical in nature. Choice
(B) is incorrect because although the passage states that Allende’s
work would have received more critical attention if the book had
been thought of as great literature, it is not clear that it would have
received more favorable reviews. Choice (C) is incorrect because
although the passage states that Allende borrowed from García
Márquez’s work, it does not state that she learned magical realism
from García Márquez. Choice (D) is the opposite of what the
passage argues. The passage suggests that it is the very subtlety of
her political message that makes Allende’s work compelling.
7.
E
The passage states, “Yet, to remember the man solely by his
associations is to miss his importance to nineteenth-century
American philosophy as a whole and to the Transcendental
Movement in particular,” which suggests the author would agree
with (A). In the second paragraph, the author refers to Alcott as a
“visionary,” which means ahead of his time, so the author would
agree with (B). In the last sentence, the author notes that Alcott
believed that “a student’s intellectual growth was concomitant with
his or her spiritual growth.” This rules out (C). In the second
paragraph, the author refers to Alcott’s ideas as polemical at the
time. Polemical means controversial, thereby implying that
Alcott’s ideas were not universally accepted, which agrees with
(D). The last paragraph of the passage praises Alcott as an erudite
orator, a point that is made in direct contrast with his lack of skills
as a writer. Therefore, (E) is not supported.
8.
B
In the first paragraph of the passage, the author states that Alcott’s
“philosophical treatises have rightly been criticized by many as
being ponderous, esoteric, and lacking focus.” The term “esoteric”
means understood by only a select group. Therefore, the correct
answer is (B).
9.
B
Choice (B) is correct. The author states that taxonomic
classifications should be used in conjunction with other
information about the animal. In (B), the team uses both observed
and accepted data, which would include classification. Choice (A)
is incorrect because the scientists use only taxonomic information.
Choice (C) is incorrect because the zookeeper uses only observed
information, ignoring the taxonomic information.
10.
B
The author tries to convey several facts and make a point about the
appropriate use of classifications. Because didactic means
“intended to instruct,” that’s pretty close. Choice (A) is incorrect
because nothing in the passage indicates that the author is upset.
Choice (C) is incorrect because the author has a definite opinion on
the matter. Choice (D) is incorrect because the author does not
sound sad. Choice (E) is incorrect because the passage does not
praise anything.
Chapter 7: Critical Reasoning
Practice: Identifying Conclusions
1.
“it is unlikely that the new defense bill will pass”
2.
“grass was not a significant part of the dinosaur diet”
3.
“automaker X will have no choice but to file for bankruptcy”
4.
“country Y will experience a decrease in obesity-related health
problems”
5.
“machines will soon outnumber humans as the number-one users of
the Internet”
Practice: Finding the Premise
1.
Premise: “A bipartisan group of 15 senators has announced that it
does not support the legislation.”
2.
Premises:
(1) “The earliest known grass fossils date from approximately 55
million years ago.”
(2) “Dinosaurs most likely disappeared from the earth around 60
million years ago.”
(3) “fossilized remains of dinosaur teeth that indicate the creatures
were more suited to eating ferns and palms”
3.
Premises:
(1) “company’s poor financial situation”
(2) “the workers at automaker X are threatening to go on strike”
4.
Premise: “the leading members of the nation’s food industry have
agreed to provide healthier alternatives, reduce sugar and fat content,
and reduce advertisements for unhealthy foods”
5.
Premise: “Recent advances in technology have led to a new wave of
‘smart’ appliances”
Practice: Locating Assumptions
1.
Conclusion: There will be no decline in enrollment at the University.
Why?
Premise: The University plans to hire two highly credentialed
biology professors to replace Professor Jones.
Assumption: That the two new biology professors will be at least as
attractive to prospective students as was Professor Jones.
2.
Conclusion: “It is unjust to charge customers under the age of 25
more to rent a car than those over the age of 25.”
Why?
Premise: “Most states allow people as young as 16 to have a driver’s
license and all states allow 18-year-olds the right to vote.”
Assumption: Because people under the age of 25 have the right to
vote and drive there is no reason to charge them more to rent a car.
3.
Conclusion: “Roughly 12.5 percent of planets in the universe should
have life on them.”
Why?
Premise: “In our solar system, there are eight planets and at least one
of them obviously has life on it.”
Assumption: All planetary systems in the universe have the same
proportion of planets with life on them as does our solar system.
4.
Conclusion: “The leaders of State A should institute the gas tax.”
Why?
Premise: “58 percent of voters in Township B approve of a proposed
2-cent gasoline tax.”
Assumption: The opinion of Township B is representative of the
opinion of all of State A.
Critical Reasoning Practice Set
1.
B
Choice (B) indicates that, overall, it may not have been financially
advantageous in 1989 for a company to move to a region with a
lower corporate tax rate. For (A), the numbers of similar
companies in regions with favorable tax policies compared with
the numbers in regions with unfavorable tax policies does not
explain why there was less corporate flight. The reference to
numbers is out of scope. For (C), both the difficulty of the codes
and the benefit to anyone other than the company are irrelevant.
Though the tax codes may have been difficult to decipher, saving
money would still have been good incentive to move. Choice (D)
would make it even harder to explain that there was less corporate
flight. Some companies would have relocated to foreign countries.
For (E), individual tax rates are out of scope.
2.
C
You need an answer that describes Tello’s response to Aramayo.
Aramayo concludes that the government should consolidate its
leadership because the government functions most efficiently when
decisions are handled by very few individuals. To make such an
argument, Aramayo must assume that there are no negative
consequences of consolidating the leadership. Tello responds by
pointing out a negative consequence. Choice (C) says that Tello
responds in such a fashion. For (A), Tello does not contradict
Aramayo’s reasoning, despite offering a possible negative
consequence. For (B), Tello does more than uncover an
assumption: Tello attacks the assumption. For (B) to be correct,
Tello’s response would have needed to have used words to the
effect “But you assume that….” For (D), Tello does not uncover
any circular reasoning. For (E), Tello does not point to any
overgeneralization.
3.
B
This is really asking for the conclusion of the argument. Choice (B)
provides the conclusion. Remember that a properly drawn
conclusion should pass the Why Test. Why would hiring a Chief
Information Officer improve productivity? Because Chief
Information Officers are like new business computer systems,
which increase productivity for companies. For (A), because the
actual function of a Chief Information Officer is never described in
the argument, you cannot conclude anything about that function.
Choice (C) contradicts the part of the passage that states “many
businesses experience dramatic gains in productivity after
installing a new computer system.” For (D), the argument provides
no basis for comparing the efficiency of a Chief Information
Officer and a new computer system. For (E), the difficulty of
measuring the results is outside the scope of this argument.
4.
B
The conclusion is that the clothes washed at the Main Street
Laundromat are cleaner than those washed at the Elm Street
Laundromat because Main Street uses more water. The premise is
that Joe’s clothes are cleaner when he does them at the Main Street
Laundromat and that Main Street’s machines use more water per
load. This is a causal argument. One way to strengthen a causal
argument is to rule out an alternate cause. Choice (B) rules out
different detergents as an alternate cause. Choice (A) is just a
restatement of the conclusion. For (C), the Oak Street Laundromat
is out of scope. For (D), how much laundry Joe does at each
Laundromat is out of scope. Choice (E) would weaken the
argument.
5.
A
The argument concludes that the change from a multiple-truck
delivery system to a single-truck system is the cause of the increase
in the rate of complaints. The premise is that the rate of complaints
increased and that there had been a change in the method of
delivery. The argument is causal. Choice (A) weakens the
argument by providing another cause for the increased rate: Today,
the complaints are being reported to the right people. This answer
choice leaves open the possibility that the actual number of
complaints is unchanged from 1964, but explains why the rate of
complaints has risen. For (B), whether any mail arrives late in a
multiple-truck delivery system is out of scope. For (C), registered
mail versus unregistered mail is out of scope. For (D), because the
argument is referring to the rate of complaints, the amount of bulk
mail is out of scope. For (E), the price of stamps is out of scope.
CHAPTER 8: VOCABULARY FOR THE GRE
Group 1 Exercises: Matching
1. C
2. J
3. E
4. G
5. A
6. L
7. K
8. B
9. N
10.
H
11.
M
12.
I
13.
D
14.
F
Group 2 Exercises: Matching
1. B
2. M
3. F
4. J
5. N
6. A
7. D
8. E
9. L
10.
C
11.
H
12.
I
13.
G
14.
K
Group 3 Exercises: Matching
1. D
2. G
3. K
4. I
5. M
6. A
7. C
8. N
9. H
10.
F
11.
E
12.
B
13.
J
14.
L
Group 4 Exercises: Matching
1. I
2. L
3. N
4. C
5. K
6. B
7. J
8. A
9. G
10.
E
11.
M
12.
D
13.
H
14.
F
CHAPTER 10: MATH FUNDAMENTALS
Math Fundamentals Drill
1. C, D, and F
To solve this problem, try writing out the possibilities. The least
prime number is 2. (2 × 2) + 3 = 7; so (C) is correct. The next
prime number is 3: (3 × 3) + 5 = 14, so (D) is correct. The next
prime number is 5: (5 × 5) + 7 = 32, which is not an answer choice.
The next prime number is 7: (7 × 7) + 11 = 60, so (F) is correct.
The next prime number is 11: (11 × 11) + 13 = 134, which is a
greater value than the answer choice possibilities. The correct
answer is (C), (D), and (F).
2. C
To answer this question, first write an equation with the
information given. So, number of cases ordered × $1,757 = total
amount of money spent. Now begin figuring out the answer to
Quantity A and the answer to Quantity B. The number of books is
equal to number of cases × 150, so it is possible to figure out how
many cases were sold. Set up the equation and solve. Cases ×
$1,757 = $10,550, so cases =
=6.004 cases. Since it is not
possible to order a partial case, only 6 cases can be ordered for
$10,550. This results in 6 × 150 = 900 books. Solve for Quantity B
in the same way. Cases × $1,757 = $12,290, so Cases =
=
6.99 cases. Since it is not possible to order a partial case, once
again, only 6 cases can be ordered and Quantity B equals 6 × 150,
or 900. The quantities are equal, and the correct answer is (C).
3. A and E
To begin, find the factors of 91: 1 and 91 or 7 and 13. Remember
that the product of two negative numbers is positive, so the integers
could also be negative factors. The question asks for the sum of the
two integers. Choice (A) is the sum of −91 and −1. Choice (E) is
the sum of 7 and 13. None of the other answer choices are possible,
so the correct answer is (A) and (E).
4. D
List all of the distinct prime integers less than 20. The prime
integers are 2, 3, 5, 7, 11, 13, 17, and 19. The problem asks for the
sum, so add all of the values up to yield 2 + 3 + 5 + 7 + 11 + 13 +
17 + 19 = 77. The ones digit is a 7, so the correct answer is (D).
5. B, C, and D
A $20 scarf can be discounted as much as 50 percent, and 50
percent of 20 is $20 ×
= $10, so the minimum sale price of a
scarf is $20 – $10 = $10. The least discount is 25 percent, and 25
percent of 20 is $20 ×
=$5, so the maximum sale price of a
scarf is $20 – $5 = $15. Therefore, the range of possible sale prices
for scarves is $10 to $15. Now, eliminate choices that fall outside
of that range: Choice (A) is less than $10, and (E) is greater than
$15, so eliminate both of them. The correct answer is (B), (C), and
(D).
6. 300
There are 3 terms in the sequence and they repeat. The question
asks about the product of the 81st, 82nd, 83rd, 84th, and 85th term.
Use the fact that the values of the terms in the sequence repeat after
every third term to determine the value of the 81st term. Divide 81
by 3 to find that there are 27 complete iterations of the sequence.
The 81st term is at the end of one of these repetitions, so its value
is −5. Therefore, the 82nd term is −2, the 83rd is 3, the 84th is −5,
and the 85th is −2. Therefore, the product is (–5) × (–2) × 3 × (–5)
× (–2) = 300. The correct answer is 300.
7. C
Recognize the Distributive Law at work here. If the expression in
Quantity A is distributed, the resulting expression is 2x + 8y, which
is the same as Quantity B. Therefore, the two quantities are equal
and the correct answer is (C).
8. A
Quantity A is the greatest number of consecutive nonnegative
integers whose sum is less than 22, so start adding the numbers
with the least value. However, Quantity A contains an important
clue with the word nonnegative. This means that the number 0
could be a value. Start with 0 and add until the sum is the greatest it
could be without exceeding 22. So 0 + 1 + 2 = 3; 3 + 3 = 6; 6 + 4 =
10; 10 + 5 = 15; and 15 + 6 = 21. Therefore, the consecutive
nonnegative integers whose sum is less than 22 are 0, 1, 2, 3, 4, 5,
and 6. That is 7 values. Quantity A is greater than Quantity B, and
the correct answer is (A).
9. D
The question asks for the greatest possible value of x + y.
Therefore, find the greatest values of x and y. The greatest value of
x is when 4 is divided by 6, which produces a remainder of 4. The
greatest value of y is when 2 is divided by 3, which produces a
remainder of 2. Therefore, the greatest value of x + y is 6, and the
correct answer is (D).
10. E
Follow the order of operations. Start with the parentheses first and
do the division and multiplication, so 12 −
− 8 × 3 = 12
− (2 − 12) − 8 × 3. Now finish the parentheses to find that the
expression is 12 –(–10) − 8 × 3. Now multiply so that the
expression is 12 – (–10) − 24. Now work the rest of the problem to
find that 22 − 24 = −2, and the correct answer is (E).
CHAPTER 11: ALGEBRA (AND WHEN TO USE
IT)
Algebra (And When to Use It) Drill
1. 19
Plug in $100 for the cost of the item to the retailer. Therefore, the
original selling price is $140, or 40 percent more than the retail
price. To find the reduced price, subtract 15 percent of $140 from
$140 to get $119. The difference between the reduced price and the
cost of the item to the retailer is then $119 – $100 = $19.
Therefore, the question is asking what percent of 100 is 19. The
correct answer is 19 percent.
2. B
First, put the equation in standard form: x2 + 8x + 7 = 0. Now
factor: (x + 7)(x + 1) = 0. Solve: x = −7 or −1. Both of the possible
values for x are negative, so Quantity B is always greater than
Quantity A.
3. 27
Because 9 = 32; the original equation becomes 33 × (32)12 = 3x; or,
33 × 324 = 3x; or, 33 + 24 = 3x. Therefore, x = 27.
4. E
Because there are variables in the answers, Plug In. Let’s make x =
10, y = 7, and c = 3. Then A = 2 × 10 – (7 − 2 × 3). Solve for the
numbers in the parentheses before subtracting. A = 20 – (7 − 6).
Therefore, A = 19. B = (2 × 10 − 7) − 2 × 3. Again, solve for the
numbers in the parentheses before subtracting. B = (20 − 7) − 6.
Therefore, B = 7. Be careful, the question is asking for A – B = 19
− 7 = 12. Plug y = 7 and c = 3 into the answers. Only (E) yields the
target, 12. Choice (C) is a trap designed to catch test-takers who
subtracted before simplifying the numbers in the parentheses.
5. A
While the relationship among the can prices is provided, no actual
numbers are supplied, so try plugging in some numbers for can
prices. A good number to choose for the cost of the large cans is
the value of the small can multiplied by the value of the medium
can, or $5 × $7 = $35. This means the medium can costs
and the small can costs
= $7,
= $5. The amount of money needed to
buy 200 medium cans is 200 × $7 = $1,400. Now PITA. Start with
(C). If the customer purchases 72 small cans, that will cost her 72 ×
$5 = $360. If she purchases 72 small cans, she also purchases 72
large cans so 72 × $35 = $2,520, which is more than the $1,400
spent on medium cans. This number is too great, so eliminate (C),
(D), and (E). Choice (B) also works out to be too great, which
leaves (A). 35 small cans × $5 a can = $175. 35 large cans × $35 =
$1,225. $1,225 + $175 = $1,400, the same price as the medium
cans. Choice (A) is correct.
6. 25
Stack and add the first two equations. Multiply the second equation
by −1.
Divide by 8 to yield k – l = 5. Multiply by 5 to yield the final
answer of 5k − 5l = 25.
7. B
This problem has a relationship between variables, so Plug In. Let
a = 2, so 3a = 6. 6 is 4 less than 10, which equals 6b. 6b = 10 yields
that b =
. a − 2b yields. − 2
= − , or − .
8. A
Work with one quantity at a time to compare them. Quantity A is
, which can be rewritten as
. This fraction can
be manipulated by moving the fraction out of the denominator;
however, that is unnecessary as the numerator and denominator are
the same thing. So
= 1, which is the value of Quantity A.
Quantity B can be simplified to
. Therefore, Quantity
A is greater, and the answer is (A).
9. B
This is a simultaneous equation question. Both quantities ask for
the value of x + y, so try to combine the equations to find that
value. If you multiply 3x + 4y = 12 by 3, the result is 9x + 12y =
36. This can be subtracted from the other equation to find that 2x +
2y = −6. Divide both sides of the equation by 2 to find that x + y =
−3. Quantity A, then, is equal to −3. Quantity B is now (–3)–2,
which can be rewritten as
. Therefore, Quantity B is greater
than Quantity A, and the correct answer is (B).
10. E
Since there are variables in the answers, Plug In. If a = 3 and b = 2,
then x = 9 and y = 18. So, 2(x + y) = 2(9 + 18) = 54. So, 54 is the
target. Now, evaluate each answer choice. Choices (A), (B), (C),
and (D) all evaluate to 54 and match the target. Choice (E),
however, equals 36. Since the question uses the word EXCEPT,
choose the answer that doesn’t match the target. Choice (E) is the
correct answer.
CHAPTER 12: REAL WORLD MATH
Real World Math Drill
1.
Plugging In your own number is a good way to tackle this. The
fractions used in the problem are
and
, and multiplying the
denominators will produce a good number with which to work.
Sadie started with 6 paintings and gave away one third of them: 6 ×
= 2. She has 4 paintings left. She then sold another half of the
original 6: 6 ×
= 3. So, she has 1 painting left, or
of the total.
2. D
When there are variables in the question stem, it’s time to Plug In.
For this problem, it’s easier to Plug In if you simplify the equation
first. Rearrange the equation to put the variables on opposite sides
of the equal sign. 8x = 4y. Then divide both sides by 4 to get that 2x
= y. Now, choose some easy numbers such as x = 2 and y = 4. In
this case, Quantity B is greater, so eliminate (A) and (C). Next, try
something like x = 0 and y = 0. In this case, the two quantities are
equal. Eliminate (B), and the correct answer is (D).
3. D
The population rankings for Year X are as follows: (1)
Massachusetts, (2) Connecticut, (3) Maine, (4) Rhode Island, (5)
New Hampshire, (6) Vermont. The rankings for Year Y are as
follows: (1) Massachusetts; (2) Connecticut; (3) Rhode Island; (4)
New Hampshire; (5) Maine; (6) Vermont. Maine, Rhode Island,
and New Hampshire have different rankings from Year X to Year Y.
4. D
In Year X, Vermont’s population is 5 percent of 15 million (or 0.75
million), and Massachusetts’ population is 40 percent of 15 million
(or approximately 6 million). 6 million is what percent of 0.75
million? Now translate: 6 million =
× 0.75 million: x = 800.
5. D
In Year X the population of Rhode Island was 10 percent of 15
million, or 1.5 million. In Year Y the population of Rhode Island
was 15 percent of 25 million, or 3.75 million. The increase was
2.25 million, or 2,250,000.
6. C
Start solving this problem by assessing all the information that is
given to you in the problem. A 20-gallon water jug is 20% full, so
there are 4 gallons in the water jug. The question is asking how
many days it will be before the jug is 85% full. 85% of 20 gallons
is 17 gallons, so that is the number we are looking for. After the
first three days 50% of the total water in the jug is added. There are
4 gallons in the jug, so after three days 2 more gallons are added to
the jug to make a total of 6 gallons. After another three days, 50%
of 6 gallons is added to the jug, so 3 gallons are added which
increases the total amount of water in the jug to 9 gallons. After
three more days, 50% of 9 gallons is added to the jug so 4.5
gallons, increasing the total to 13.5 gallons. After another three
days the total is increased by 50% of 13.5, which is 6.75 gallons,
which will increase the total to more than 17 gallons. So there were
4 increases of three days apiece, for a total of 12 days, (C).
7. A
This is an average question, so make an Average Pie any time the
word average is used. Begin by figuring out how many supporters
of the referendum are in each town. The question states that there is
an average of 3,500 supporters in Towns B and D, so there is a total
of 3,500 × 2 = 7,000 supporters in these towns. The question also
states that Town B has 3,000 supporters, so the number of
supporters in Town D is 7,000 − 3,000 = 4,000. Additionally, the
question states that there is an average of 5,000 supporters in
Towns A and C, so there is a total of 5,000 × 2 = 10,000 supporters
in these towns. It’s also stated that Town A has 3,000 supporters, so
the number of supporters in Town C is 10,000 − 3,000 = 7,000.
Now, compare the quantities. Quantity A is the average number of
supporters for Towns C and D, and Quantity B is the average
number of supporters for Towns B and C. Because both quantities
use Town C, and both quantities ask for an average, those values
cancel out and all that remains is to compare the number of
supporters in Towns B and D. There are 3,000 supporters in Town
B and 4,000 in Town D, so Quantity A is greater and the correct
answer is (A). Alternatively, solve for the average given in both
quantities. However, the result is the same; the correct answer is
(A).
8. E
Plug In The Answers, starting in the middle with (C). If each A
employee was given $740, each C employee was given half of that,
or $370. Each B employee received one-and-a-half times the C
raise, so 1.5 × $370 = $555. Now calculate the total money spent
on raises. 50 A employees got $740 each, for a total of 50 × $740 =
$37,000. 100 B employees got $555 each, for a total of 100 × $555
= $55,500. 150 C employees got $370 each: 150 × $370 = 55,500.
These add up to a total of $148,000, but the problem says that the
total raise amount is $500,000. You need a much bigger answer.
Rule out (A), (B), and (C). Try skipping directly to (E). If the A
workers got $2,500, the C workers got $1,250, and the B workers
got $1,875. 50 × $2,500 = $125,000; 100 × $1,875 = $187,500; and
150 × $1,250 = $187,500. Because these numbers add up to
$500,000, (E) is correct.
9. B
Median means middle. In other words, if you put all the ninthgraders in order by score, the middle student would have the
median score. Thinking in terms of percentiles, the 50th percentile
is the middle, so on the ninth-grade pie chart, whatever score
includes the 50th percentile when you put the scores in order is the
median score. According to the chart, 16 percent of the ninthgraders scored below 65, and 37 percent scored between 65 and 69
points. 16 percent + 37 percent = 53 percent. The 50th percentile,
then, falls within the group that received 65–69, so 65–69 is the
median score.
10. A
In 1995 there were 1,350 + 950 + 625 + 500, or ≈ 3,400 students in
grades 9 through 12. 3,400 is 35 percent of School District X, so
3,400 =
⋅ x, x ≈ 9,700, so there were 9,700 students.
11. E
There were 1,200 ninth-graders in 2013. 25 percent of them, or
300, scored in the 70–79 point range. 14 percent, or 168, scored in
the 80–89 point range. The difference between 300 and 168 is 132.
Choice (E) is the closest.
12. D
Draw a Ratio Box for each ratio. Solution X has 2 parts a and 3
parts b, for a total of 5 parts. Solution Y has 1 part a and 2 parts b,
for a total of 3 parts. Solution Z has 3 parts X and 11 parts Y, for a
total of 14 parts. There are 630 ounces of Solution Z, which yields
a multiplier of 45, and leads to 495 ounces of Solution Y and 135
ounces of Solution X. A total of 495 ounces of Solution Y yields a
multiplier of 165, which further yields 165 ounces of a from
Solution Y. A total of 135 ounces of Solution X yields a multiplier
of 27, which further yields 54 ounces of a from Solution X. 165 +
54 = 219 ounces of a. The correct answer is (D).
CHAPTER 13: GEOMETRY
Geometry Drill
1. A, B, and C
You need to check if the two angles in each answer choice can be
part of a right triangle. A right triangle has a 90-degree angle, and
because the sum of all the angles of a triangle is 180 degrees, the
sum of the other two angles must equal 180 − 90 = 90 degrees. In
(A), 20 + 70 = 90 degrees, so these could be the other two angles in
a right triangle. Choices (B) and (C) also add up to 90 degrees, and
so they are correct as well. In (D) and (E), the two angles have a
sum greater than 90 degrees, so they are incorrect.
2. B
To find the perimeter of the figure, you need to add up all of its
external sides. However, this is a funny-shaped figure, so begin by
making the figure into two familiar shapes. Draw a horizontal line
to separate the figure into a triangle and a rectangle. The side of the
rectangle is now equal to the hypotenuse of the right triangle. So,
use the triangle to find the missing side. To find the hypotenuse of
the right triangle recognize the common right triangle (5 : 12 : 13),
or use the Pythagorean theorem (52 + 122 = x2). The missing side
of the rectangle is 13. Therefore, the perimeter equals 5 + 12 + 17
+ 13 + 17 = 64. Choice (A) is the perimeter without the missing
side of the rectangle. If you chose (D), you included an interior side
of the rectangle.
3. A
We know that the triangle EFG is equilateral because all three
angles are equal. That means all of its sides equal 8. From the first
equation, we know that the sides of the square also equal 8. The
area of the square is s × s = 8 × 8 = 64, which is greater than
Quantity B.
4. D
Draw it on your scratch paper, and plot the points. Both a and b
must be positive, but their values could be equal or unequal.
Quadrant I has (+, +) coordinates, Quadrant II has (–, +)
coordinates, Quadrant III has (–, –) coordinates, and Quadrant IV
has (+, –) coordinates.
5. E
There are variables in the answers, so Plug In. If the shorter piece
is 2 yards long, then the longer piece is 3(2) + 2 = 8 yards and t
must be 2 + 8 = 10. The target answer, the length of the longer
piece, is 8. Plug in 10 for t into all of the answers. Choice (E) is the
only answer choice that matches your target of 8.
6. D
If CD, the radius of the smaller circle, is 3, then the diameter of the
smaller circle is 6. The diameter of the smaller circle is equal to the
radius of the larger circle because the smaller circle touches the
center and the edge of the larger circle. The formula for the area of
a circle is πr2, so the area of the larger circle is 36π. To find the
area of the semicircle, divide by 2 to find 18π.
7. 2
Draw it! If Karl starts x meters below the boat and swims straight
down for 8 meters, he is now x + 8 meters below the boat. He
swims 24 meters to his right and then swims 26 meters in a direct
line back to the boat. This drawing should look like a triangle with
sides x + 8, 24, and a hypotenuse of 26. Use the Pythagorean
theorem to solve for x, or using special right triangles, realize that
this is a 5, 12, 13 triangle multiplied by 2. x + 8 has to equal 10, so
x = 2.
8. A
This is a Plug In problem. Make r = 2. The circumference of the
circle will be 4π, which is approximately 12. The perimeter of the
square is 2 + 2 + 2 + 2 = 8. Quantity A is greater. Try plugging in
other numbers and you will see that Quantity A will always be
greater.
9. C
The area of the circle is 25π, so the radius of the circle is 5. This
means that both AC and BC have length 5, and angles A and B are
equal to each other. Because angle C is 60° and the total angle
measure of a triangle is 180°, the sum of angle A and B must be
120°. Thus, each angle in triangle ABC is 60°, making this an
equilateral triangle. An equilateral triangle has equal sides and
equal angles, so the only possible length of the triangle legs is 5.
10. A
Remember the third side rule. The third side of a triangle must be
less than the sum of the other two sides of a triangle, but greater
than the difference. That gives us a clear range for x. It must be
greater than 6 but less than 12. Quantity A, therefore, is greater
than Quantity B; the answer is (A).
11. A
You can see that the two triangles are almost the same, except that
the base length in the triangle to the right is slightly larger.
Remember, you cannot trust the figure to be drawn to scale. If you
look at these triangles and expand the base length, the triangle on
the right starts to collapse and its height gets smaller and smaller.
Thus, height f must be greater than height g. This technique works
quite well in a number of GRE quant comp geometry problems!
12. B
In order to find the x-coordinate of a point on a line, you must first
find the slope of the line. Notice that along with points A and B, the
origin is also a point on the line in the figure. Using the coordinates
of (0, 0) and A (2, 3), the slope is
= . Because the slope
of a line stays constant, you can use the value you just found to
solve for the missing x-coordinate of point B. Using points A (2, 3)
and B (x, 4.2), solve
= . Cross-multiply to find that 3(x
− 2) = 1.2(2), so 3x − 6 = 2.4 and 3x = 8.4. Therefore, x = 2.8, and
the correct answer is (B).
13. A
Use the 3 : 4 : 5 ratio or the Pythagorean theorem to determine that
the length of AB is 4. Because the area of a triangle equals ×
base
× height, triangle ABD has an area of
× 3 × 4, or 6. Be wary of
(D), which is the area of the rectangle.
14. B
Because the two angles have the same measure, the wedges of the
circle they mark off will have the same area. The triangle is smaller
than the wedge, so Quantity B is greater than Quantity A.
15. C
Because LMNO is a parallelogram and ∠OLM = 108°, ∠LON must
be 180° − 108° = 72°. ∠LON is the same fraction of the entire
circle (360 degrees) that arc AB is of the entire circumference, so
= . Thus, arc AB is
of the circumference. So,
× 15π = 3π.
CHAPTER 14: MATH ET CETERA
Et Cetera Drill
1. C
If there is one more red marble than blue, there must be 7 blue
marbles and 8 red ones, for a total of 15. The probability of
choosing a blue marble is
, or
. If you selected
(E), you probably computed the probability of drawing a red
marble rather than the probability of drawing a blue one.
2. D
Plug the values into the function. First, find ¥(5): (5 × 10 − 1) = 49.
Next, find ¥(3) = (3 × 10 − 1) = 29. Now subtract them: ¥(5) – ¥(3)
= 49 − 29 = 20.
3. B
First, eliminate (D) as both quantities are numbers. Next, rewrite
the function without the negative exponent. Negative exponents are
used as another way to write a reciprocal—for all x ≠ 0, x-n =
So, this function can be rewritten as # x = 2-x =
Quantity A is #8 =
. Because
>
=
.
. Therefore,
and Quantity B is #4 =
=
, Quantity B is greater. The correct answer
is (B).
4. 20
Remember, in this problem order matters, so do not divide! Any of
the 5 finalists could be awarded “Best in Show.” There are 4
choices left for “Honorable Mention,” because a different dog must
be chosen. Therefore, the total number of possibilities is 5 × 4, or
20.
5. A
Use the group equation: Group 1 + Group 2 – Both + Neither =
Total. So, $40,000 + $30,000 – $15,000 + Neither = $90,000. Thus,
$55,000 + Neither = $90,000. So, the company budgets $35,000 on
other products. Quantity A is greater than Quantity B.
6. B
List the two-digit prime numbers less than 50: 11, 13, 17, 19, 23,
29, 31, 37, 41, 43, and 47. The numbers in which the tens digit is
greater than the units digit are 31, 41, and 43. Because 3 out of the
11 possibilities meet the requirement, (B) is correct.
7. A
Plug In the Answers, starting with (C). With 9 staff members, the
elected official has
options. This works out to
126, which is too large. Try plugging in (A). With 7 staff members,
the elected official has
= 21 different groups of
5 from which to choose.
8. E
Plug In: Make x = 2 and y = 3. Now x # y = 2(2 − 3) = −2. Watch
out for traps: Choices (A) and (C) will give you −2, but because the
question asks for x # (x # y), you need to perform the operation
again. 2 # (–2) = 2[2 – (–2)] = 2(4) = 8. Now put x = 2 and y = 3
into the answer choices to find a match for your target answer, 8.
Be sure to eliminate (A), (B), (C), and (D) as soon as you realize
they are negative. The only answer that matches is (E).
9. B
Use a Ratio Box to find that if there are twice as many yellow as
green and 12 total, then there are 8 yellows and 4 greens. Two
situations would fit the requirements of the problem: Pull out a
yellow and then green, or pull out a green and then yellow. So, find
the probability of each of these situations; then add these two
probabilities together. The probability of yellow and then green is
. The probability of green and then yellow is
. Add these two probabilities to find
.
10. B
You could try to draw this all out, but it is easier to do the math.
For Quantity A, if you’re creating triangles, you’re really choosing
three points from the set of 10. This is a combination problem—
order doesn’t matter, because triangle ABC would be the same as
triangle BCA. You could use the formula
= 120. For
Quantity B, note that quadrilaterals are any four-sided figures, so
you’re just choosing 4 points from 10. You could use the formula
for combinations:
= 210. The correct answer is (B).
Comprehensive Math Drill
1. B
Any line that is tangent to a circle makes a 90 degree angle with the
radius of that circle at the point of tangency. The radius of the
circle is 5, so the length of line segment AC is also 5. The side
opposite the 90 degree angle is BC and this measures
. If you
know the special right triangles, you should be able to recognize
that the sides are in the ratio of a 30 : 60 : 90 triangle. The ratio of
the sides in a 30 : 60 : 90 triangle is x : x
: 2x, respectively. If 2x
=
, then x =
. Multiplying
by
side of the triangle is 5. Since the x
yields that the x
side of a 30 : 60 : 90 is
longer than the x side, AC is longer than AB, and Quantity B is
greater. If you didn’t see the side relationship, you could always
use the Pythagorean Theorem to find the length of AB. Either way,
the correct answer is (B).
2. C
Plug In. Let x = 2. Quantity A is
simplifies to
× , which yields
. Quantity B is
, which
. The quantities are equal, so
eliminate (A) and (B). Plug In again. Let x = 1. Quantity A is
Quantity B is
, which also yields
.
. To be certain, check the
other possibilities in FROZEN. The correct answer is (C).
3. C
Remember that the percentages for standard deviations are 34
percent, 14 percent, 2 percent in both directions from the mean. If
the mean is 50, then 34 percent score between 50 and 54, 14
percent score between 54 and 58, and 2 percent score above 58.
The same idea applies in the other direction: If the mean is 50, then
34 percent score between 50 and 46, 14 percent score between 46
and 42, and 2 percent score below 42. So, both quantities are equal
to 2 percent.
4. A
The equation y = mx + b describes a line where m is the slope and b
is the y-intercept—the place where the line crosses the y-axis.
Hence, the y-intercept of our line, or P, is (0, 1), which means the
length of OP is 1. Because Q is on the x-axis, the y-coordinate must
be 0, and we can use the line equation to solve for x: 0 = − x + 1,
so −1 = −
x, and x =
. That means OQ =, and Quantity A is
greater. Because this is a quant comp, though, we can actually
compare the quantities without solving them. If you recognize from
the line equation that our slope is − , and you remember that slope
is defined as
, you might also recognize that Quantity A, OQ, is
our run, and Quantity B, OP, is our rise. Disregarding the negative
sign—distance is always an absolute value, and therefore positive
—we can see that our rise is less than our run, and Quantity A is
greater.
5. B
For Quantity A, “pairs” tells you that you’re picking two and that
order does not matter so divide. You could use the formula
= 190. For Quantity B, the “rankings” tells you that order matters,
so do not divide. So, you could use the formula 10 × 9 × 8 = 720.
6. D
The denominator is the same for both expressions, so we only need
to compare numerators to determine which fraction is greater. Plug
in to see whether kl is greater than or less than 1. Let k = 0.5 and l
= 1.5. Therefore, kl = 0.75. Eliminate (B) and (C). Now let k = 10
and l = 10, kl = 100. Eliminate (A).
7. A
Find all the factors of 78. 78 = 1 × 78 = 2 × 39 = 3 × 26 = 6 × 13.
The greatest odd factor is 39; the greatest prime factor is 13.
Quantity A is greater than Quantity B.
8. 4
If Joe starts with $200 and spends $150 on a CD player, he has
only $200 – $150 = $50 left. Each CD is $12, so divide $50 by
$12. It goes in 4 times with $2 left over. Don’t round! Joe can buy
only 4.
9. A
For triangle ABC, the base is the difference between A and C, 1.
Finding the height is a little more difficult. The height of a triangle
is any perpendicular line dropped from the highest point to the
level of the base. The height does not need to touch segment AC as
long as it extends from B to the level of AC. For this triangle,
distance from B to the origin is the height, 4. Plug in the base and
height: Area =
× 1 × 4 = 2.
10. A
When you have a large number that needs to be divided, the best
way to begin answering the question is to break that number down
into its prime factors. So 10(96) = 2 × 5 × (32)6, or 2 × 5 × 312.
Therefore, the prime factorization of any number that 10(96) can be
divided by can contain no more than one 2, one 5, and twelve 3s.
Only (A), 90, meets these requirements. For example, the prime
factorization of (D), 540, includes two 2s so 10(96) is not divisible
by 540. Choice (A) is correct.
11. B and C
Roberta’s rate is 50 miles in 2 hours. Notice that the first number in
this proportion is greater than the second. Use that to eliminate (A)
and (D). For (B),
proportion. For (C),
, so this is the same as the original
, so this is also the same as the
original proportion. Choice (E) does not produce this same
proportion, so eliminate it as well.
12. C
There were seven cities with temperatures in Year Y higher than or
equal to those in Year X: Baltimore, Detroit, Las Vegas,
Minneapolis, New York, Phoenix, and San Francisco.
13. C
The lowest average temperature was 34° F in Anchorage, and the
highest was 83° F in Las Vegas. Percent change
=
144 percent, which is closest to (C).
14. C
You’re averaging the highs and lows for Years X and Y, so the
number of things is 4. The bar shows the average of Years X and Y,
which reads 60. Multiply 60 by 4 to get the total, 240. Get the
average high temperatures for Years X and Y from the straight and
dotted lines on the chart. They’re about 103 degrees and 97
degrees. The total is 240 = 103 + 97 + low Year X + low Year Y. If
you subtract the highs from the total, you’re left with 40 degrees as
the total for the lows. Because you want the average of the lows,
divide this total by 2. The closest answer is 20°.
15. A, B, and C
First, simplify the inequality by subtracting 2 from both sides: |2x −
3| > 5. Now plug each answer choice into the inequality to see
which value of x makes the inequality true. The correct values are
those in (A), (B), and (C).
16. A
The question states that x is an odd integer, so eliminate (C)
because 0 is not odd. Simplify x + y + z < z by subtracting z from
each side: x + y < 0. Because x is less than y, x must be negative so
that when added to y, the answer will be less than zero. Therefore,
eliminate (D) and (E). Now plug in the remaining answers to see
which value of x will work in the inequality. Choice (A) is the only
choice that works.
17. E
First, solve for x by multiplying 4 by itself until you get 1,024. This
means that x equals 5. If you substitute 5 for x in the second
equation, the equation reads, 46 × 54. Because the answers are
expressed in terms of 4n, 5n, and 10n, expand out 46 × 54 to get 4 ×
4 × 4 × 4 × 4 × 4 × 5 × 5 × 5 × 5. Now try to express it using 10n.
We need to factor two of the fours and rewrite this as 4 × 4 × 4 × 4
× 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5. Now, convert this back into
exponents to get 44 × 24 × 54, or 44 × 104.
18. D
First, use the volume formula to find the width: V = l × w × h. So,
780 = 12 × w × 5. Thus, the width is 13. Next, draw the figure.
Notice that the greatest distance is from one corner to the opposite
corner, such as from the front left bottom corner diagonally to the
rear right top corner. You can use the formula for diagonal of a
rectangular solid, a2 + b2 + c2 = d 2, in which a, b, and c are the
dimensions of the rectangular solid and d is the diagonal, and love
that you have a calculator. Thus, (5)2 + (12)2 + (13)2 = d 2. So, 25 +
144 + 169 = d 2, and thus d
= or 13
.
19. D
There are six spots to fill. Because no boys can sit on the ends of
the bench, only the 3 girls are available to fill one spot at one end
of the bench. Once one girl has been chosen to fill that spot, there
are 2 girls available to fill the spot on the other end of the bench.
Then, there are 4 children (boys and girls) available to fill the other
four spots. Because 3 × 4 × 3 × 2 × 1 × 2 = 144, (D) is correct.
20. C
Use the Average Pie. If 16 is the average of 3 numbers, their total is
48. You know that one of the numbers is 24, so p + q + 24 = 48.
Thus, (p + q) = 24. You need to find 16(p + q), so find 16(24),
which equals 384.
Part VI
Practice Tests
18 Practice Test 1
19 Practice Test 1: Answers and Explanations
20 Practice Test 2
21 Practice Test 2: Answers and Explanations
TEST INSTRUCTIONS
It’s important to become familiar with the instructions for the test now, so that
you don’t waste time figuring them out on test day.
General Instructions
Each exam consists of six sections—two Analytical Writing sections, two
Verbal Reasoning sections, and two Quantitative Reasoning sections. The
Analytical Writing sections will always be first. The Verbal and Quantitative
Reasoning sections may appear in any order. You will have 30 minutes for
each Analytic Writing section, 30 minutes for each Verbal, and 35 minutes for
each Quantitative Reasoning section. If desired, you may take a 10-minute
break after Section 4. Remember that during the actual test, there may be an
additional verbal or quantitative experimental section.
Section 1
30 minutes
Analytical Writing
Section 2
30 minutes
Analytical Writing
Section 3
30/35 minutes
Verbal or Quantitative Reasoning
Section 4
30/35 minutes
Verbal or Quantitative Reasoning
Section 5
30/35 minutes
Verbal or Quantitative Reasoning
Section 6
30/35 minutes
Verbal or Quantitative Reasoning
When taking a Verbal or Quantitative Reasoning section, you are free to skip
questions that you might have difficulty answering and come back to them
later during the time allotted for that section. You may also change your
response to any question in a section during the time allotted to work on that
section. You may not go back to an earlier section of the test after time for
that section runs out.
Need More Practice?
The Princeton Review’s
1,007 GRE Practice
Questions offers drills for
every question type, along
with detailed, comprehensive
explanations.
Analytical Writing Instructions
Issue Topic
You will be given a brief statement on an issue of general interest and specific
instructions on how to respond to that issue. You will have 30 minutes to plan
and write a response in which you develop a position on the issue. Make sure
that you respond to the specific instructions and support your position on the
issue with reasons and examples drawn from such areas as your reading,
experience, observations, and/or academic studies.
Before you begin writing, you may want to think for a few minutes about the
passage and the instructions and then outline your response. Be sure to
develop your analysis fully and organize it coherently. Leave a minute or two
at the end to reread what you have written and make any revisions you think
are necessary.
Argument Topic
You will be given a short passage that presents an argument, or an argument
to be completed, and specific instructions on how to respond to that passage.
You will have 30 minutes to plan and write a response in which you analyze
the passage. Note that you are NOT being asked to present your own views on
the subject. Make sure that you respond to the specific instructions and
support your analysis with relevant reasons and/or examples.
Before you begin writing, you may want to think for a few minutes about the
passage and the instructions and then outline your response. Be sure to
develop your analysis fully and organize it coherently. Leave a minute or two
at the end to reread what you have written and make any revisions you think
are necessary.
Verbal Reasoning Instructions
Each Verbal Reasoning section is 30 minutes long and has 20 questions. For
some questions, you will be instructed to choose one or more answer choices.
The instructions may or may not specify the number of answers you must
choose. If the number of answers is specified, you must choose all of the
correct answers in order to have your response counted as correct. If the
number is not specified, choose all that correctly answer the question. No
credit will be given if fewer or more than all of the correct answers are
chosen.
Quantitative Reasoning Instructions
Each Quantitative Reasoning section is 35 minutes long and has 20 questions.
You will be provided with a five-function calculator—one with addition,
subtraction, multiplication, division, and square-root features—during
Quantitative Reasoning sections.
For some questions, you will be instructed to choose one or more answer
choices. The instructions may or may not specify the number of answers you
must choose. If the number of answers is specified, you must choose all of the
correct answers in order to have your response counted as correct. If the
number is not specified, choose all that correctly answer the question. No
credit will be given if fewer or more than all of the correct answers are
chosen.
Some questions will require you to enter your own answer. If the question
provides a single response space, enter a single number. You may enter
negative signs and decimal points. If the question tells you to round your
answer, do so. Otherwise, enter the entire answer. If the question provides two
response spaces, you must enter your answer in the form of a fraction. You
are not required to enter fractions in their most reduced form. If you are aware
of more than one correct response, you should enter only one of them.
Some questions will ask you to fill blanks in the text by clicking to select
from a list of choices. Sometimes all of the choices will be used, and
sometimes only some of the choices will be used. The correct answer always
requires you to put a different choice in every blank.
Note on Numbers and Figures
Numbers: All numbers used are real numbers.
Figures: The position of points, angles, regions, and so on can be assumed to
be in the order shown, and angle measures can be assumed to be positive.
Lines shown as straight can be assumed to be straight. Figures can be
assumed to lie in a plane unless otherwise indicated. Any other figures are not
necessarily drawn to scale, unless a note states that a figure is drawn to scale.
Chapter 18
Practice Test 1
Click here to download a PDF of Practice Test 1.
SECTION 1: ISSUE TOPIC
Directions:
You will be given a brief quotation that states or implies an issue of general interest and specific
instructions on how to respond to that issue. You will have 30 minutes to plan and compose a response
in which you develop a position on the issue according to the specific instructions. A response to any
other issue will receive a score of zero.
“Governments are justified in circumventing civil laws when doing so is vital to the protection of
national security.”
Write an essay in which you take a position on the statement above. In developing and supporting
your position, you should consider ways in which the statement might or might not hold true.
SECTION 2: ARGUMENT TOPIC
Directions:
You will be given a short passage that presents an argument, or an argument to be completed, and
specific instructions on how to respond to that passage. You will have 30 minutes to plan and compose a
response in which you analyze the passage according to the specific instructions. A response to any
other argument will receive a score of zero.
Note that you are NOT being asked to present your own views on the subject. Make sure that you
respond to the specific instructions and support your analysis with relevant reasons and/or examples.
The following is from a recent email from the Diord Corp. Human Resources Manager: “Tobor
Technologies found that mental health problems and mental illness were responsible for about 15
percent of employee sick days. Tobor amended its employee insurance plan so that workers receive
the same coverage for mental illness as they do for physical illness. In addition, the company hired
an on-site psychologist and created a system that allows workers to schedule confidential counseling
appointments. After one year, the number of sick days used by employees declined by 10 percent.
Diord Corp. has had an increase in employee sick days over the past two years, so we should
introduce a similar insurance plan and counseling program. These measures will surely reduce
employee absenteeism and cause an increase in productivity.”
Write a response in which you examine the argument’s unstated assumptions, making sure to explain
how the argument depends on the assumptions and what the implications are if the assumptions
prove unwarranted.
SECTION 3: QUANTITATIVE REASONING
For each of Questions 1 to 7, compare Quantity A and Quantity B, using additional information
centered above the two quantities if such information is given. Select one of the four answer choices
below each question and fill in the circle to the left of that answer choice.
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
A symbol that appears more than once in a question has the same meaning throughout the question.
1 of 20
AB is parallel to CD.
BC is parallel to AD.
Quantity A is greater.
Quantity B is greater.
Quantity A
Quantity B
s
t
The two quantities are equal.
The relationship cannot be determined from the information given.
2 of 20
A certain punch is created by mixing two parts soda and three parts ice cream. The soda is 4 parts sugar,
5 parts citric acid, and 11 parts other ingredients. The ice cream is 3 parts sugar, 2 parts citric acid, and
15 parts other ingredients.
Quantity A
Parts sugar in the punch
Quantity B
Parts citric acid in the
punch
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
3 of 20
The average (arithmetic mean) high temperature for x days is 70 degrees. The addition of one day with a
high temperature of 75 degrees increases the average to 71 degrees.
Quantity A
Quantity B
x
5
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
4 of 20
Each angle in ∆QRS has a degree measurement of either x or y and 2x + y = 180.
Quantity A
Quantity B
Perimeter of QRS
17
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
5 of 20
The scores for the 500 students who took Ms. Johnson’s final exam have a normal distribution. There
are 80 students who scored at least 92 points out of a possible 100 total points and 10 students who
scored at or below 56.
Quantity A
Quantity B
The average (arithmetic
mean) score on the final
exam
87
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
6 of 20
AB is parallel to CD.
AD is parallel to BC.
2AD = EG
Quantity A
The area of ABCD
Quantity A is greater.
Quantity B
The area of EFG
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
7 of 20
(3x − 4y)(3x + 4y) = 2
Quantity A
Quantity B
9x2 − 16y2
4
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
8 of 20
If 8a − 2 = 22, then 4a − 1 =
2
11
12
44
9 of 20
Twenty percent of the sweaters in a store are white. Of the remaining sweaters, 40 percent are brown,
and the rest are blue. If there are 200 sweaters in the store, then how many more blue sweaters than
white sweaters are in the store?
10 of 20
=
0
1
4
12
16
Questions 11 through 14 refer to the following graph.
11 of 20
What was the total number of subscriptions for Newsmagazine x during the year in which
Newsmagazine x accounted for 14.6 percent of nationwide news magazine subscriptions?
1,020
1,980
6,300
7,000
7,200
12 of 20
In which of the following years did subscriptions to Newsmagazine z account for approximately
of
the total nationwide magazine subscriptions?
2009
2006
2003
2000
1997
13 of 20
What was the approximate percent increase in nationwide subscriptions to newsmagazines between
1995 and 1996 ?
4%
11%
26%
51%
73%
14 of 20
In 1998, what was the approximate number of subscriptions to newsmagazines nationwide?
3,000
13,000
16,000
20,000
67,000
15 of 20
If a = (27)(3−2) and x = (6)(3–1), then which of the following is equivalent to (12)(3–x) × (15)(2–a) ?
5(–2245)(320)
5(24)(38)
5(2245)(320)
16 of 20
Jill has received 8 of her 12 evaluation scores. So far, Jill’s average (arithmetic mean) is 3.75 out of a
possible 5. If Jill needs an average of 4.0 points to get a promotion, which list of scores qualifies Jill to
receive her promotion?
Indicate all such lists.
3.0, 3.5, 4.75, 4.75
3.5, 4.75, 4.75, 5.0
3.25, 4.5, 4.75, 5.0
3.75, 4.5, 4.75, 5.0
17 of 20
In the figure above, if RSTU is a rectangle, what is the value of a + b + c + d + e + f ?
18 of 20
If the probability of selecting, without replacement, 2 red marbles from a bag containing only red and
blue marbles is
and there are 3 red marbles in the bag, what is the total number of marbles in the
bag?
10
11
55
110
165
19 of 20
All first-year students at Blue State University must take calculus, English composition, or both. If half
of the 2,400 first-year students at Blue State University take calculus and half do not, and one-third of
those who take calculus also take English composition, how many students take English composition?
400
800
1,200
1,600
2,000
20 of 20
If
is an integer, which of the following represents all possible values of x ?
0 ≤ x ≤ 10
0<x<9
0 ≤ x < 10
1 ≤ x ≤ 10
1 < x < 10
SECTION 4: VERBAL REASONING
For questions 1 through 6, select one entry for each blank from the corresponding column of choices.
Fill all blanks in the way that best completes the text.
1 of 20
The professor is a noteworthy intellect, and as a teacher she shows more (i)____________ than her
colleagues, whose teaching skills are (ii)____________ procedure.
2 of 20
It would be (i)____________ for our leaders, given their responsibilities as democratically elected
officials, to neglect to do everything they could to (ii)____________ an entirely (iii)____________
problem.
3 of 20
Despite her mentor’s advice that she attempt to sound consistently ____________, the graduate student
often resorted to using slang when presenting significant parts of her thesis, her habitual speech patterns
overriding her years of learning.
4 of 20
Although she felt Steve (i)____________ the subtlety of the delicious stew recipe with his addition of
the sweet potato, she thought the pungent onion (ii)____________ the otherwise (iii)____________
taste combination.
5 of 20
At first, a still-life painting can appear quite (i)____________, its focus on such everyday objects as
flowers or fruits apparently uninspired. In the hands of (ii)____________ painter, however, careful
attention to slight shifts of color and texture can lead to a truly (iii)____________ and exemplary
painting.
6 of 20
The leaders of Ukraine’s “Orange Revolution” were a study in contrasts. At the center of the political
storm stood Viktor Yushchenko, his once (i____________ face transformed into a monstrous mask by
dioxin poisoning; but, at his side, no one could miss the (ii)____________ Yulia Tymoshenko, soon to
become the world’s only prime minister to adorn the covers of fashion magazines.
For each of Questions 7 to 11, select one answer choice unless otherwise instructed.
Questions 7 through 9 are based on the following reading passage.
In analyzing the poetry of Mona Feather, we are confronted with three different yardsticks by
which to measure her work. We could consider her poems as the product of a twentieth-century artist in
the tradition of James Joyce, T.S. Eliot, and Wallace Stevens. However, to do so would be to ignore a
facet that informs every word she writes and that stems from her identity as a woman. Yet, to
characterize her solely as a woman poet is to deny her cultural heritage, for Mona Feather is also the
first modern poet of stature who is also an American Indian.
Stanley Wilson has argued compellingly that the huge popularity Feather enjoys among the Indian
reservation school population of the United States is creating a whole new generation of poetry
enthusiasts in an age when the reading of poetry is on the wane. While this is undoubtedly true, Mr.
Wilson’s praise gives the impression that Feather’s readership is limited to her own culture—an
impression which hints that Mr. Wilson is himself measuring her by only one criterion. Radical feminist
writers have long found in Feather’s poetry a sense of self-pride which strikes a chord with their own
more political philosophies. Her imagery, which always made use of the early Native American
traditions in which the woman had an important role, was seen as the awakened sensibility of a kindred
spirit.
Yet for all the “feminist” touches in her writing, it would be a disservice to consign Feather to the
ranks of politicized writers, for her message is deeper than that. The despair that characterized
twentieth-century modern poets is to be found in Mona Feather’s work as well; she writes of the
American Indians of the 1930s confined to ever-shrinking reservations and finds in that a metaphor for
all of modern mankind trapped on a shrinking earth of limited resources.
7 of 20
The primary purpose of the passage is to
describe the work of Mona Feather
compare Feather with Joyce, Eliot, and Stevens
show Feather’s roots in her Native American heritage
argue that Mona Feather’s work can be looked at in several different ways
discuss the women’s movement in America
8 of 20
The passage implies that the author believes Stanley Wilson’s view of Feather is
a compelling and complete assessment of her work
focused too much on her status as a Native American poet
meant to disguise his opinion of Feather as a poet lacking in talent
critical of Native American children’s literary judgment
based on all major themes and images in her poetry
9 of 20
The author mentions James Joyce, T.S. Eliot, and Wallace Stevens in order to
compare the political messages in Feather’s work to those in the work of other authors
highlight the radical differences between male and female poets in the twentieth century
contrast Feather’s thematic choices with those of her contemporaries
enumerate a list of artists whose sensibilities made them Feather’s kindred spirits
describe a critical context in which Feather’s work can be analyzed
Questions 10 through 11 are based on the following reading passage.
Among the more interesting elements of etymology is the attempt to derive the meaning of
seemingly nonsensical expressions. Take, for instance, the increasingly archaic rural phrase “to buy a
pig in a poke.” For centuries, the expression has been used to signify the purchase of an item without
full knowledge of its condition. It relates to the common Renaissance practice of securing suckling pigs
for transport to market in a poke, or drawstring bag. Unscrupulous sellers would sometimes attempt to
dupe purchasers by replacing the suckling pig with a cat, considered worthless at market. An
unsuspecting or naïve buyer might fail to confirm the bag’s contents; a more urbane buyer, though,
would be sure to check and—should the seller be dishonest—“let the cat out of the bag.”
10 of 20
Consider each of the choices separately and select all that apply.
Which of the following phrases from the passage would help the reader infer the meaning of the word
urbane as used in context?
“increasingly archaic rural phrase”
“without full knowledge”
“unsuspecting or naïve buyer”
11 of 20
Select the sentence in which the author provides a definition for an antiquated term that may be
unfamiliar to the reader.
For questions 12 through 15, select the two answer choices that, when used to complete the sentence, fit
the meaning of the sentence as a whole and produce completed sentences that are alike in meaning.
12 of 20
Although she was such a bad-mannered child that she was sent to a boarding school, as an adult she is
the very model of ____________.
friendliness
diffidence
propriety
reticence
decorum
brashness
13 of 20
Politicians sometimes appear to act in a manner that is almost ____________; however, when all the
information is released after the fact, it is apparent that they were acting according to a deliberate plan.
pithy
conventional
conformist
whimsical
flawless
capricious
14 of 20
Forced to take an alternate road when a massive oil spill closed the highway, the two-hour detour made
their already arduous trip even more ____________.
irksome
onerous
facile
glib
implacable
immutable
15 of 20
Though many of her contemporaries found her odd, Ella Wilkins is now much admired for her
____________ spirit, especially her willingness to reject prevailing feminine roles and to travel to
foreign lands alone.
forlorn
magnanimous
adventurous
bellicose
desolate
doughty
For each of Questions 16 to 20, select one answer choice unless otherwise instructed.
16 of 20
Microfiber synthetics have been taking the place of natural fibers in an ever-increasing number of
clothes because they provide the same durability and deplete fewer natural resources. A shirt made of
microfiber synthetics is, however, three times as expensive to produce as a natural-fiber shirt. It follows
that the substitution of microfiber synthetic clothes for natural-fiber clothes is, at this time, not
recommended from a financial standpoint.
Which of the following statements, if true, most seriously weakens the argument?
A microfiber synthetic shirt costs one-half the price of a natural-fiber shirt to maintain.
The production of microfiber synthetic clothes necessitates garment factories to renovate
obsolete machinery and to hire extra workers to operate the new machines.
The upkeep of natural-fiber shirts is far less expensive than the upkeep of any other naturalfiber garment in current production.
While producers anticipate that the cost of microfiber synthetics will remain stable, they
recognize that the advent of recycling programs for natural fibers should bring down the costs
of natural fibers.
The cost of providing stain guards for microfiber synthetic shirts would probably be greater
than what garment producers now spend on stain guards for natural-fiber shirts.
Questions 17 through 18 are based on the following reading passage.
Scholars of early Buddhist art agree that Buddha images in human form emerged around the first
century A.D. in the regions of Mathura, located in central India, and Gandhara, now part of Pakistan and
Afghanistan. Uncertainty exists, however, about whether Mathura or Gandhara has the stronger claim to
primacy. Those who believe that anthropomorphic sculptures of the Buddha first appeared in Gandhara
point out that earlier Buddhist art was largely aniconic and that bas relief was far more common than
sculpture. They argue that Greek influence in Gandhara promoted the development of the new style and
form of representation of the divine. Other scholars make the case for indigenous development of such
representations in Mathura, citing a centuries-long record of iconic art in pre-Buddhist traditions. They
do not reject all foreign influence, but they argue that local traditions provided a strong foundation for
the development of Buddhist sculpture.
Art historians bolster their arguments by highlighting distinctive features of the sculptures from
each region. For example, the artists of Gandhara sculpted their Buddhas in heavy, pleated drapery,
similar to that of Greek statues. Wavy lines indicating hair also reflect Greek influence. Mathura
Buddhas, on the other hand, are portrayed wearing lighter robes draped in a monastic style, often with
part of the shoulder and chest left bare. Elongated earlobes and strong facial features characterize
Mathura images of the Buddha, whereas Gandhara images possess more angular features. Sorting out
dates and directions of influence has proven difficult, but the totality of evidence suggests that the
Buddha image evolved simultaneously in both regions and was shaped by the predominant cultural
influences in each region.
17 of 20
Which of the following, if true, would those who believe that anthropomorphic images of Buddha
originated in Gandhara be likely to cite as evidence for their viewpoint?
Pre-Buddhist subcultures in the Gandhara region created representations of their deities in
human form.
Mathuran Buddhas’ lightweight robes appear to have been modeled on the real robes of people
who lived in a warm climate.
Gandharan artists were isolated from the larger society and not exposed to influences from
outside the region.
Rulers from the Mathura region had political ties to Greek rulers and frequently exchanged gifts
with them.
The hairstyles worn by Gandharan Buddhas are similar to those depicted on Greek pottery from
the same period.
18 of 20
According to the passage, Buddhist art
first appeared in regions that are now part of India, Pakistan, and Afghanistan
experienced a period during which human representations of the Buddha were not common
characteristically portrayed figures with elongated earlobes and strong facial features
began to appear in the medium of bas relief as a result of Greek influence
was more influenced by foreign artworks than by indigenous artistic traditions
Questions 19 through 20 are based on the following reading passage.
In 1887, Eugene Dubois began his search in Sumatra for the “missing link”—the being that would
fill the evolutionary gap between ape and man. He discovered a fossilized human-like thighbone and a
section of skull. He confirmed that these fossils were of significant age by examining other fossils in the
same area. The thighbone’s shape indicated that it belonged to a creature that walked upright. Dubois
estimated the size of the creature’s skull from the skull fragment and concluded that this creature’s brain
volume was between that of the higher primates and that of current humans. Although the concept of
“missing link” has changed dramatically and a recent analysis showed Dubois’s fossils to be far too
recent for humans to have evolved from this “missing link,” the value of his discovery and the debate it
generated is unquestionable.
19 of 20
Consider each of the choices separately and select all that apply.
The passage supplies information to answer which of the following questions?
What was the approximate age of the fossils found by Dubois?
Does Dubois’s find meet current definitions of the “missing link”?
Do the flaws in Dubois’s conclusions invalidate his work?
20 of 20
Select a sentence in which the author reaches a conclusion.
SECTION 5: QUANTITATIVE REASONING
For each of Questions 1 to 7, compare Quantity A and Quantity B, using additional information
centered above the two quantities if such information is given. Select one of the four answer choices
below each question and fill in the circle to the left of that answer choice.
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
A symbol that appears more than once in a question has the same meaning throughout the question.
1 of 20
A circle with center R has a radius of 6 and is inscribed in square ABCD.
Quantity A
Quantity B
The area of the largest
triangle that can be drawn
inside square ABCD
The area of the circle with
center R
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
2 of 20
xy ≠ 0
= 632 and
= 158
Quantity A
Quantity B
x
y
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
3 of 20
Quantity A
Quantity B
The remainder when 135
is divided by 7
The remainder when 135
is divided by 19
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
4 of 20
a and b are integers.
a2 = b3
Quantity A
Quantity B
a
b
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
5 of 20
ab < 0
bc > 0
Quantity A
Quantity B
ac
0
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
6 of 20
|x| = 6
y=x+4
Quantity A
Quantity B
y
10
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
7 of 20
A rectangular ribbon of width x is wrapped around the circumference of a right circular cylinder of
radius n, encircling the cylinder without overlap as shown in the figure above. The area of the ribbon is
equal to the area of the base of the cylinder.
Quantity A
Quantity B
x
n
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
8 of 20
List A: 1, 2, 7, 8, 15, 2, 3, 5, 6, 13
x is the median of the even numbers in List A.
y is the median of the prime numbers in List A.
z is the median of the least and greatest numbers in List A.
Quantity A
Quantity B
The median of 2x, y, and z
z
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
9 of 20
Oil is pumped from a well at a rate of 500 gallons per hour. How many gallons of oil are pumped from
the well in 3 hours and 15 minutes?
10 of 20
A certain pet store sells only dogs and cats. In March, the store sold twice as many dogs as cats. In
April, the store sold twice the number of dogs that it sold in March, and three times the number of cats
that it sold in March. If the total number of pets the store sold in March and April combined was 500,
how many dogs did the store sell in March?
80
100
120
160
180
11 of 20
In the xy-plane, rectangle WXYZ has vertices at (–2, −1), (–2, y), (4, y), and (4, −1). If the area of WXYZ
is 18, what is the length of its diagonal?
3
3
3
3
3
12 of 20
How many three-digit integers can be created using only 5 distinct digits?
10
15
20
30
60
13 of 20
At Megalomania Industries, factory workers were paid $20 per hour in 1990 and $10 per hour in 2000.
The CEO of Megalomania Industries was paid $5 million in 1990 and $50 million in 2000. The percent
increase in the pay of Megalomania’s CEO from 1990 to 2000 was what percent greater than the percent
decrease in the hourly pay of Megalomania’s factory workers over the same period?
850%
900%
950%
1,700%
1,900%
Questions 14 through 16 refer to the following graph.
14 of 20
If there were 38 child safety organizations and the funds contributed to these organizations in September
1989 were evenly distributed, how much did each charity receive?
$12,000,000
$9,400,000
$2,500,000
$250,000
$38,000
15 of 20
From September 1985 to December 1989, what was the approximate ratio of private donations for
homeless aid to private donations for animal rights?
20 : 9
3:2
4:3
5:4
6:5
16 of 20
Which of the following charitable causes received the least percent increase in private donations from
September 1989 to October 1989 ?
Animal Rights
Disaster Relief
Homeless Aid
Environmental Protection
Child Safety
17 of 20
In the repeating decimal 0.0653906539…, the 34th digit to the right of the decimal point is
9
6
5
3
0
18 of 20
If 3x + 2y = 24, and =
, then y =
19 of 20
If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 12, what is the greatest possible
integer value of x ?
8
11
23
28
44
20 of 20
If AB = BC, which of the following is an expression for the area of quadrilateral ABDE ?
a2 – b2
SECTION 6: VERBAL REASONING
For questions 1 through 6, select one entry for each blank from the corresponding column of choices.
Fill all blanks in the way that best completes the text.
1 of 20
Many fashions that were considered daring in their time have been so widely worn and imitated that the
(i)____________style is no longer seen as (ii)____________.
2 of 20
Western culture has so influenced Middle Eastern music that even the latter’s roles of composer and
performer, at one time inseparable, have now begun to ____________.
3 of 20
Kazan was quickly (i)____________by many of his contemporaries for his transgression, who saw his
testimony as treachery, an act of (ii)____________ which stained how they viewed him both as an artist
and as a man. It was only by continually making films that he was able to (iii)____________ his
perceived sins and achieve some measure of atonement.
4 of 20
Although tranquilizers usually have a ____________effect, this is not always the case, especially when
the abuse of these drugs results in a failure to induce the much-desired sleep.
5 of 20
As a rule, (i)____________interpretations of events are rejected by modern scientists in their attempts
to find secular insights into the matrix of causes and effects in our modern world. Paradoxically, this
fact does not (ii)____________the existence of individual scientists who possess views that may be
(iii)____________with a belief in supernatural causes.
6 of 20
The Johnsons were not known for their (i)____________; at the very least, none of the family members
was fearful of (ii)____________, of appearing or acting differently from other people.
For each of Questions 7 to 12, select one answer choice unless otherwise instructed.
Questions 7 through 10 are based on the following reading passage.
According to most scientists, the universe began approximately 10 to 15 billion years ago and has
been expanding ever since. This theory, known as the Big Bang theory, is the fairly direct result of
Hubble’s law, which states that objects farther away from Earth are receding faster than those closer.
This expansion implies a singular point which all matter is expanding from.
Complicating the scientific explanation is that the Big Bang cannot be thought of as an explosion
from some identifiable source—rather, space and time were created in the Big Bang. Furthermore, the
relationship between distance and speed is not precisely linear. So, if one were to think of galaxies as
particles created in a big bang, these galaxies have both a local component of motion, as well as playing
a role in the overall expansion of the universe.
A further complication is that galactic distances are so great that galactic motion, even if the
galaxies are moving at incredible speeds, is difficult to observe. Scientists must therefore rely on a
“standard candle,” an object of known brightness within the galaxy they wish to observe. Using the
inverse square law, scientists can then measure how far that galaxy is away from our own. For instance,
suppose a supernova in galaxy A appears one hundred times as bright as one in galaxy B. By the inverse
square law, galaxy B is ten times farther away than galaxy A, assuming, of course, that distance is the
only factor affecting brightness.
7 of 20
It can be inferred from the sentence highlighted in the passage that a standard candle is useful to
scientists for which of the following reasons?
Standard candles do not have their own locus of motion.
Standard candles more reliably adhere to the law of inverse squares than do other supernovas.
Only standard candles provide a known measure of brightness.
Knowledge of an object’s brightness allows scientists to measure the speed at which the object
is moving toward Earth.
Knowledge of an object’s brightness allows scientists to accurately measure its distance from
Earth.
8 of 20
Consider each of the choices separately and select all that apply.
According to the passage, if two astronomical objects of differing distances from Earth were observed,
which of the following would be true of the object closer to Earth?
It would not be as bright as the object farther from Earth.
It would be younger than the object farther from Earth.
It would be traveling away from the Earth more slowly than the farther object.
9 of 20
It can be inferred from the passage that a standard candle may not provide an accurate measure of
distance if
the galaxy being measured is moving too quickly
interstellar dust makes the object measured appear dimmer than it really is
if the galaxy being measured has a local component of measurement
the particles being measured do not completely accord with a linear motion
the galaxies being measured move at different speeds
10 of 20
According to the passage, if two supernovas are observed and one of those supernovas is brighter than
the other, scientists can conclude that
the brighter supernova is moving closer to our galaxy at a higher speed
the precise location of the supernova is measurable
the brighter supernova may be closer to our own galaxy
the brighter supernova is farther away from Earth by a distance that is roughly inversely
proportional to the dim supernova
the distance between the supernovas and our own galaxy is inversely proportional
Questions 11 through 12 are based on the following reading passage.
Throughout the twentieth century, it was accepted as fact that cells in our brains, called neurons, do not
regenerate. Research by neurologist Elizabeth Gould overturned this core doctrine within the span of a
few years. Her experiments on rats showed that even after suffering severe trauma, their brains were
able to heal themselves by regenerating neurons. Gould’s findings have incited a flood of new research
into applications that may take advantage of neurogenesis.
One such study examines the role of reduced neurogenesis among individuals suffering from
depression. It is speculated that neurogenesis may contribute to an explanation for the so called “Prozac
lag.” As an antidepressant, the immediate boost of serotonin caused by Prozac should have had
instantaneous mood elevating effects. However, patients suffering from depression only begin to
experience mood elevation weeks after beginning treatment. The study speculates that during this
period, the brain may be regenerating neurons.
11 of 20
The author mentions the “Prozac lag” primarily in order to
raise a possible objection to a newly proposed theory
present a situation for which a new theory may serve an explanatory role
offer evidence that runs counter to a previously held belief
suggest a counterexample that undermines a newly proposed theory
provide supporting evidence that a newly discovered phenomenon may have unforeseen
effects
12 of 20
In the second paragraph, select the sentence in which the author describes an unexpected observation.
For questions 13 through 16, select the two answer choices that, when used to complete the sentence, fit
the meaning of the sentence as a whole and produce completed sentences that are alike in meaning.
13 of 20
Plato, an important philosopher, is primarily known because he wrote down Socrates’s ____________
conversations. It is through Plato’s record of these dialogues that Socrates’s teachings have survived and
continue to enlighten seekers of wisdom.
inspiring
edifying
tedious
grating
rousing
didactic
14 of 20
Even the colossal meal failed to ____________her voracious appetite.
cadge
exacerbate
provoke
satiate
mendicate
allay
15 of 20
Slicks of oil on a rain-soaked street are ____________ and beautiful, but the lovely rainbows they
produce on the asphalt can seem rather ugly when one reflects upon the road hazards they create and the
environmental damage they entail.
anodyne
iridescent
monocoque
pavonine
parietal
saturnine
16 of 20
He had not always been so callous, but with time he became ____________to the violence around him.
adorned
cauterized
sensitized
ostracized
inured
attuned
For each of Questions 17 to 20, select one answer choice unless otherwise instructed.
17 of 20
When the maker of Megapower, a vitamin supplement, modified its formula two years ago, Tasmania,
an island off the coast of New Zealand, suffered a decrease in its export earnings. Tasmania’s only
export, kiwi fruit, constitutes a substantial portion of the world supply of that fruit. Researchers
concluded that the old Megapower formula contained natural kiwi extract, but the new formula does
not.
Which of the following, if true, gives the strongest support for the researchers’ claim?
Some South American countries have begun to grow kiwi fruit successfully.
United States chemists have started development of a synthetic kiwi extract.
The manufacturers of Megapower chose not to renew their contract with the Tasmanian kiwi
growers.
Imports of kiwi fruit have fallen in the country where Megapower is manufactured.
There was a marked drop in sales of a number of formerly profitable items that used kiwi as an
ingredient.
Questions 18 through 20 are based on the following reading passage.
While art historians do not necessarily agree on the date of the birth of modern art, they do agree
that mid-nineteenth century French art shows a clear and distinct break from tradition. Pressed to point
to a single picture that represents the vanguard of the modern art movement, art historians will often
point to Courbet’s The Painter’s Studio.
The peculiar subtitle of Courbet’s work, “Real allegory summing up a seven-year period of my
life” confirms that Courbet was striving to do something strikingly original with his work. The
argument has been made that the painting struck a blow for the independence of the artist, and that since
Courbet’s work, artists have felt freed from the societal demands placed upon their work. Paintings prior
to Courbet’s time were most often focused on depicting events from the Bible, history, or literature.
With his singular painting, Courbet promulgated the idea that an artist is capable of representing only
that which he can experience through his senses of sight and touch; the true artist will then be compelled
to make his representation as simply and directly as possible.
18 of 20
Which of the following would most effectively replace the word promulgated as it is used in the context
of the passage?
Displayed
Disseminated
Proclaimed
Concealed
Secreted
19 of 20
Select the sentence in the passage that best explains the effect of Courbet’s work on other artists.
20 of 20
The effect that Courbet had on painting is most analogous to which situation?
An avant-garde writer who subverts novelistic conventions
A machinist who tinkers and improves his invention
A watercolor painter who paints in the same style as his peers
A scientist who comes up with a unified theory of several discordant scientific ideas
A seamstress who makes a ball gown using several different types of fabric
Chapter 19
Practice Test 1: Answers and
Explanations
INTERPRETING YOUR RESULTS
After you check your answers on the following pages, fill out this sheet to
interpret your results.
Analytical Writing
To evaluate your performance on the Analytical Writing sections, compare
your response to the advice and samples in the Analytical Writing chapter.
Verbal Reasoning
Refer to the explanations to check your answers. Count the number of
questions you got correct in each Verbal Reasoning section, and calculate the
total number correct. Find the section of the Interpretive Guide (below) that
corresponds to your total to get an idea of how your performance compares to
that of other test takers.
Test 1
# Correct
Section 4
Section 6
Total
Quantitative Reasoning
Refer to the explanations to check your answers. Count the number of
questions you got correct in each Quantitative Reasoning section, and
calculate the total number correct. Find the section of the Interpretive Guide
(below) that corresponds to your total to get an idea of how your performance
compares to that of other test takers.
Test 1
# Correct
Section 3
Section 5
Total
Interpretive Guide
The table below provides a guide for interpreting your performance based on
the number of questions you got correct in each subject.
Section 3
1. A
Point C has the same x–coordinate as point D, so s = 8. Point C
also has the same y-coordinate as point B, so t = 7. That means that
Quantity A is greater.
2. A
The punch is made with two parts soda and three parts ice cream.
This means that in one mixture if you added two parts of soda, then
that’s 4 × 2 = 8 parts sugar and 5 × 2 = 10 parts citric acid. If you
added three parts ice cream, then that’s 3 × 3 = 9 parts sugar and 2
× 3 = 6 parts salt. There’s 8 + 9 = 17 total parts sugar and 10 + 6 =
16 total parts citric acid. There’s more sugar than citric acid.
Choice (A) is correct.
3. B
This is a Quant Comp question with variables, so Plug In more
than once. To easily compare the two quantities, recycle the
number in the problems by Plugging In x = 5. This problem
involves averages, so draw an average pie. If x = 5, and the average
high temperature over the course of 5 days is 70 degrees, then the
total temperature for the 5 days is 5 × 70 = 350. The problem states
that one additional day has a high temperature of 75 degrees, so
draw another average pie. There are now six days and the total high
temperature is 350 + 75 = 425 and the average high temperature for
the six days is =
= 70 . This is less than the 71 degree average
specified in the problem. Because the two quantities cannot both
equal 5, eliminate (C). If it is unclear whether the value for x needs
to be greater or less than 5 to make the average high temperature at
the end of the problem equal to 71 degrees, Plug In again. This
time, try a number less than 5, such as x = 4. If x = 4, then the total
temperature for 4 days with an average of 70 degrees is 4 × 70 =
280. The addition of one day with a high temperature of 75 degrees
means that the total high temperature is 280 + 75 = 355 over the
course of 5 days. Therefore, the average is
= 71. Therefore, the
correct value of x is 4 and so the value of Quantity A is 4. This is
less than the value of Quantity B, so the correct answer is (B).
4. D
Because ΔQRS is isosceles, side RS must be equal to one of the
other sides, and x could measure 4 or 7. Thus, the perimeter could
be 4 + 4 + 7 = 15, or the perimeter could be 4 + 7 + 7 = 18. You
can’t tell if the perimeter is greater or less than 17, so the answer is
(D). Remember, you cannot trust the figure to be drawn to scale!
5. B
Remember that a normal distribution curve has divisions of 34
percent, 14 percent, and 2 percent on each side of the mean. 80 out
of 500 is 16 percent, or 14 percent + 2 percent, and 10 out of 500 is
2 percent. Draw a normal distribution curve and label it. There are
three standard deviations between 92 and 56, so 92 − 56 = 36, and
36 ÷ 3 = 12. The mean is 92 − 12 = 80, which is smaller than
Quantity B.
6. C
Plug in numbers for the sides. Let AD = 4, so EG = 8. Let l = 3.
The area of ABCD = 3 × 4 = 12, and the area of EFG = (3 × 8) =
12. The two quantities can be equal, so eliminate (A) and (B). Try
changing your numbers, and you will see that the two quantities
will always be equal.
7. B
FOIL out the equation given, and you’ll get (3x − 4y)(3x + 4y) =
9x2 − 16y2, so Quantity A is 2. Quantity B is therefore bigger, and
the answer is (B).
8. C
Solve for a by adding 2 to each side to get 8a = 24. Divide by 8 to
find a = 3. Plug a = 3 into the second equation to find 4(3) − 1 = 12
− 1 = 11. Alternatively, you could save yourself some time by
noticing that 8a − 2 is 2(4a − 1). If 2(4a −1) = 22, divide by 2 to
get 4a − 1 = 11.
9. 56
Twenty percent of the sweaters in the store are white, so there are
200 ×
= 40 white sweaters. There are 200 − 40 = 160 sweaters
remaining. Of the remaining sweaters, 160 ×
= 64 are brown.
That means that 160 − 64 = 96 are blue. There are 96 − 40 = 56
more blue sweaters than white sweaters.
10. D
Because 412 is a common factor of both 413 and 412, you can
rewrite the numerator as 412(4 − 1). Now look at the whole
fraction:
. You can divide 412 by 411, leaving you with
41(4 − 1). Now the calculation should be much easier: 4 × 3 = 12,
(D).
11. D
Refer to the right side and the left side of the “Subscription to
Newsmagazine x, 1995–2010” chart. In 2005, Newsmagazine x
accounted for 14.6 percent of newsmagazine subscriptions, and it
had 7,000 subscriptions.
12. B
In 2006, Newsmagazine z accounted for 9,400 out of 57,000
newsmagazine
subscriptions.
Therefore,
Newsmagazine
accounted for approximately 9,000 out of 57,000, or
z
, of the
nationwide newsmagazine subscriptions.
13. D
In 1995, there were 1,500 subscriptions to Newsmagazine x, which
accounted for approximately 25 percent of total nationwide
subscriptions. Total nationwide subscriptions in 1995, then, were
equal to about 6,000 (25 percent of total nationwide subscriptions =
1,500). Using the same process, total nationwide subscriptions in
1996 were equal to about 9,000 (30 percent of total nationwide
subscriptions = 2,600). The percent increase between 1995 and
1996 is
or
, or 50 percent.
14. C
In 1998, Newsmagazine x had 3,300 subscriptions, or 20.5 percent
of the total number of newsmagazine subscriptions. Set up the
calculation to find the total: 3,300 =
16,000.
x. Solve it to find that x =
15. C
a = 27 ×
= 3, and x = 6 ×
= 2. Find (12)(3–x)(15)(2–a) = (12)
(3–2)(15)(2–3) =
. Now, reduce: =
.
16. B and D
Use the Average Pie to find that Jill’s mean of 3.75 for 8
evaluations gives her a current total of 3.75 × 8 = 30 points. Use
the Average Pie to find that if she needs an average of 4.0 for 12
scores, she needs 4.0 × 12 = 48 total points. Jill still needs 48 − 30
= 18 points. Her four remaining scores must total 18 or greater.
Only (B) and (D) have a total of at least 18.
17. 270
To answer this question remember that each angle in a rectangle is
90 degrees and there are 180 degrees in a triangle. Look at the
figure. When presented with a shape like this, look for shapes that
are familiar. The rectangle has been divided into 4 separate
triangles. Three of the triangles have one side of the triangle that is
represented by the angle of the original rectangle. For example, a
triangle is represented by the angles of a and b as well as the 90
degree angle that is represented by point S. Since there are 180
degrees in a triangle, and 90 of those degrees are found at point S,
the sum of angles a and b is 90. The same principle can be applied
to the triangle that is created by angles c, d, and point T, as well as
the triangle created by angles e, f, and point U. Since this is true, c
+ d = 90 and e + f = 90. Therefore, the sum of all the angles is 270.
18. B
Plug In the Answers, starting with (C). If the total is 55, then the
probability would be
, which does not equal
. The
denominator is too large, so try choice (B). If the total is 11, then
the probability is
, which reduces to
.
19. D
Use the Group formula: Total = Group1 + Group2 – Both + Neither.
In this problem, the total is 2,400. The question also states that
1,200 students (half of the total) take calculus, so that is Group1;
one-third of that group (400) take both calculus and English.
Because every student takes calculus or English or both, the
Neither group is zero. Solve for the number of students who take
English by plugging these numbers into the group formula: 2400 =
1200 + Group2 − 400. The number of students who take English is
1,600, or (D).
20. A
To solve this expression you need to break apart the factorial of 13
to the common prime number in the denominator, in this case the
number 2. 13! can be expressed as 13 × 12 × 11 × 10 × 9 × 8 × 7 ×
6 × 5 × 4 × 3 × 2 × 1. When you break apart this factorial into its
prime numbers you are left with 13 × 11 × 7 × 52 × 35 × 210. For a
fraction to result in an integer, the denominator of the fraction must
share at least one prime factor with the numerator. The greatest
number of 2s that can be found in the prime factorization of 13! is
10, so x ≤ 10. Eliminate (B), (C), and (E). Now for the tricky part!
Any nonzero number raised to the power 0 is 1. Since the result
when any integer is divided by 1 is also an integer, 0 must be
included in the range of possible x values. The answer is (A).
Section 4
1. prowess and maladroit
The first blank has a strong clue, so begin there. The blank is
describing the professor…as a teacher and gives further insight
that she shows more…teaching skills then her colleagues. The
transition word and indicates that there is consistency between her
description as a noteworthy intellect and her skills as a teacher.
Therefore, a good word for the first blank is “skills.” Choice (A),
prowess, is a good match for skills so keep (A). Choice (B),
profligacy, means reckless extravagance and (C), orthodoxies,
means beliefs. Eliminate (B) and (C). The second blank is
describing the professor’s colleagues…teaching skills. The
sentence gives further insight by stating that the professor shows
more skills than her colleagues. Therefore, a good word for the
blank is “unskilled” or “not good.” Choice (D), spurious, means
fake which is not a match for “unskilled” so eliminate (D). Choice
(E), maladroit, is a good match for the blank, so keep (E). Choice
(F), eclectic, means from different sources, so eliminate (F). The
correct answer is (A) and (E).
2. irresponsible, forestall, and avoidable
The keys to the first blank are the clues “given their responsibilities
as democratically elected officials” and “neglect to do everything
they could.” These clues indicate that the first blank should have a
negative connotation; a word that means something as simple as
bad would eliminate thoughtful and intuitive, leaving irresponsible.
Blanks (ii) and (iii) build on the idea set up in the first half of the
sentence. The second blank describes the action that would be bad,
so use something that means solve. Sustain and cultivate are the
opposites of what’s needed for the second blank, leaving forestall.
The last blank describes the type of problem, and entirely suggests
it’s a solvable problem. Avoidable is close, and it helps the whole
sentence make sense.
3. erudite
Despite is a transition word that implies a contrast between the
student’s actual behavior when presenting her thesis and her
mentor’s advice. The student resorted to using slang, language that
is informal and unscholarly. Therefore, the word in the blank must
mean formal or scholarly. The only word that fits that description
is erudite, which is the best choice. The other answer choices can
be used to describe speech, but none of these words contrast the
mentor’s advice with the student’s use of slang.
4. augmented, overwhelmed, and delicate
Start with the second blank. The clue pungent tells you this onion
did something bad to the delicious stew. Exaggerated and satiated
are positive; overwhelmed is the only fit. The transition otherwise
tells you to change direction from the third blank’s clue of pungent.
Look for a word that means subtle or soft. Only delicate fits. For
the first blank, the clue is that Steve’s stinky onion hurt the delicate
stew. The transition although tells you to change direction. So, this
addition of the sweet potato was good. Only augmented fits.
5. banal, an adept, and sublime
The first clue is its focus on such everyday objects as flowers or
fruits apparently uninspired, so the first blank has to mean
something such as “uninspired.” Banal, which means predictable,
matches this. For the second blank, the painter must pay careful
attention, so the second blank must mean “careful” or “talented,”
which matches an adept. Since the painting is exemplary, the third
blank must be sublime.
6. comely and prepossessing
The first blank describes Viktor Yuschenko’s face. The clue is that
his face was transformed into a monstrous mask by dioxin
poisoning and the transition word once tells us an appropriate word
for the blank would be the opposite of monstrous; something like
attractive would work nicely. Quiescent means calm, and fatuous
means foolish, so those words don’t work. Comely, which means
attractive, is the only word that works. The second blank is
describing Yulia Tymoshenko. Both the transition phrase a study in
contrasts and the clue about fashion magazines suggest that a word
that means beautiful is appropriate. Though it might not sound like
it, prepossessing does, in fact, mean beautiful. Felicitous means
well-expressed, and decorous means full of propriety, so although
they are both positive words, they aren’t as fitting here as the
credited response is.
7. D
According to the first sentence, her work can be viewed three
different ways. The rest of the passage describes those ways: as the
work of a modern poet, of a woman, and of a Native American.
Choice (A) is too vague, and the passage doesn’t so much describe
her work as how it should be viewed. Choices (B) and (C) are too
narrow and don’t describe the overall purpose. Choice (E) doesn’t
match the passage.
8. B
In the second paragraph the author states, “Mr. Wilson’s praise
gives the impression that Feather’s readership is limited to her own
culture—an impression which hints that Mr. Wilson is himself
measuring her by only one criterion,” which best fits (B). Choices
(A) and (E) contradict the passage and are too broad and extreme.
Choice (C) contradicts the passage, and (D) is not supported.
9. E
The second sentence of the passage claims, “We could consider her
poems as the product of a twentieth-century artist in the tradition of
James Joyce, T.S. Eliot, and Wallace Stevens.” Thus, the author
mentions Joyce, Eliot, and Stevens in order to describe one context
—twentieth-century poetry—in which Feather’s work can be
analyzed. Eliminate (A) because the author doesn’t compare
Feather’s political messages to those of these authors. Eliminate
(B) because the author doesn’t use these authors to discuss
differences between male and female poets. Eliminate (C) because
the author doesn’t contrast Feather’s themes with those of these
authors. Although Joyce, Eliot, and Stevens were, like Feather,
twentieth-century artists, the passage doesn’t say that they shared
sensibilities, which eliminates (D). Choice (E) is the answer.
10. C
Only (C) provides a clue to the meaning of urbane as used here:
The urbane buyer is contrasted with the “unsuspecting or naïve
buyer,” so it must mean “not unsuspecting” or “not naïve.” Choice
(A) tantalizingly dangles the word “rural” before our eyes, trying to
take advantage of that word’s well-known association with the
word urban. Urbane, though, means sophisticated. Moreover, if
(A) were accepted, the strangely illogical proposition that citydwellers knew best how to buy animals at market would have to be
accepted as well. Choice (B), thankfully, presents no such
difficulties of interpretation and appears in the definition of the
obscure expression itself, not in the comparison between
unsuspecting and urbane.
11.
It relates to the common Renaissance practice of securing
suckling pigs for transport to market in a poke, or drawstring
bag.
In this sentence the author defines the term “poke” as a drawstring
bag. This is the only instance in which the author gives a definition
for a word that the reader may not be familiar with because the
word “poke” is not a common term used to describe a drawstring
bag.
12. propriety and decorum
The clue is “was such a bad-mannered child.” Time acts as a
change-of-direction transition (“as an adult”) that indicates the
blank should mean something like well-mannered. Only propriety
and decorum mean well-mannered. Diffidence, reticence, and
brashness are all traits that would be considered bad-mannered.
Friendliness does not necessarily mean well-mannered.
13. whimsical and capricious
The blank describes how politicians act. The clue is “acting
according to a deliberate plan.” The change-of-direction transition
however tells you that they appear not to have a plan. Words that
mean unplanned or random should be in the blank. Both whimsical
and capricious fit this meaning. Conventional and conformist have
the opposite meaning. The other two words are unrelated to the
blank.
14. irksome and onerous
The transition even more tells you to stay in the same direction as
the clue. “Forced to take an alternate road,” “two-hour detour,” and
“arduous trip” tell you that the journey was difficult. Put a word
that means hard or tiring in the blank. Only irksome and onerous fit
this meaning. Facile and glib describe something easy, and
implacable and immutable describe something that doesn’t change.
15. adventurous and doughty
The transition especially tells you to stay in the same direction as
the clue “willingness to reject prevailing feminine roles and to
travel to foreign lands alone.” Thus, she has a bold spirit. Only
adventurous and doughty mean bold. Although she is traveling
alone, there is nothing to support that she is lonely, as forlorn and
desolate suggest. Magnanimous and bellicose do not fit.
16. A
The argument concludes that the substitution of microfiber clothes
for those made from natural fabrics is not financially sound. The
premise is that microfiber clothes last as long as natural fabric
clothes but are three times as expensive to produce. The argument
assumes that there are no other factors that need to be considered to
evaluate the cost effectiveness of switching. Choice (A) points out
another factor that would affect the overall costs and so weakens
the argument. Choice (B) helps to explain why the microfiber
synthetic shirt is more expensive to produce than a natural fiber
shirt, but it does not weaken the argument. In (C), comparing
natural fiber shirts and other fiber garments is not relevant. Choice
(D) strengthens the argument. Choice (E), by pointing out
additional costs associated with microfibers, also strengthens the
argument.
17. E
The first paragraph presents the Gandhara-first view that “Greek
influence in Gandhara promoted the development of the new style
and form of representation of the divine.” The second paragraph
provides evidence Gandharan Buddhas shared certain features with
Greek art. Choice (E) provides additional information about those
similarities and is the best choice. Choices (A) and (C) undermine
the idea that Gandharan artists were responding to outside
influences. Choice (B) is irrelevant, and (D) provides evidence for
outside influences in Mathura.
18. B
The first sentence says that “images in human form emerged
around the first century A.D.,” and the middle of the first paragraph
states that “earlier Buddhist art was largely aniconic.” You can
conclude from these statements that the earliest Buddhist art didn’t
usually depict the Buddha in human form. Eliminate (A); although
human representations first appeared in these regions, the passage
doesn’t say that the first Buddhist art appeared in the same places.
The passage doesn’t support (C), (D), and (E).
19. B and C
For (A), the passage says only that the age of these fossils was “far
too recent for humans to have evolved” from them. This does not
give an age for the fossils. The last sentence says that “the concept
of ‘missing link’ has changed dramatically,” which answers the
question in (B). The last sentence also answers the question in (C)
because it says, “the value of his discovery and the debate it
generated is unquestionable.”
20.
Although the concept of “missing link” has changed
dramatically and a recent analysis showed Dubois’s fossils to be
far too recent for humans to have evolved from this “missing
link,” the value of his discovery and the debate it generated is
unquestionable.
In the last sentence, the author states that the value of Dubois’s
fossils is “unquestionable.” This statement represents the author’s
conclusion.
Section 5
1. B
Draw the figure. You have a square with a circle inside of it that
has a radius of 6. Therefore, the length of one side of the square is
12. Quantity A asks for the area of the largest triangle that can be
drawn inside the square. The largest triangle cuts the square in half
diagonally (subsequently creating a 45 : 45 : 90 triangle) and has a
height and base of length 12. So the area of the triangle is
(12)
(12) = 72. Quantity B is asking for the area of the circle with center
R. So the area of the circle is 62π, or 36π. π is approximately 3, so
you know that 36 times 3 is greater than 72. Quantity B is greater.
2. D
There are a lot of variables in this problem, so starting thinking
about Plugging In. The variable a has to be the same for each
equation. You cannot pick just any number, however, because you
must satisfy the equations. When you feel stuck on a problem, start
looking at the numbers; remember the math will always work out
nicely. Examining the two equations you realize that 158 × 4 =
632, so these two numbers are related. So the easiest number to
plug in for a is 632. Now you know that xs = 1, and ys = 4. Since
the variable s is the same in both equations, they cancel each other
out and you are left with x = 1 and y = 4. Eliminate (A) and (C).
Next, try a FROZEN number such as a = −632. In this case, xs =
−1 and ys = −4 or x = −1 and y = −4. Eliminate (B). The correct
answer is (D).
3. C
135 ÷ 7 = 19, remainder 2. 135 ÷ 19 = 7, remainder 2. Both
Quantity A and Quantity B equal 2.
4. D
Plug In. Let a = 8 and b = 4. Quantity A can be greater than
Quantity B, so eliminate (B) and (C). Now let a = b = 1. Quantity
A can be equal to Quantity B, so eliminate (A).
5. B
Plug in numbers for a, b, and c. If a = −2, b = 3, and c = 4, then ac
= −8. Quantity B is greater; eliminate (A) and (C). If a = 2, b = −3,
and c = −4, then ac is still negative. Quickly consider different
numbers, but realize that Quantity A will always be negative.
6. D
If |x|=6, then x = 6, or x = −6. If x = 6, then y = 6 + 4 = 10. The
quantities are equal, so you can eliminate choices (A) and (B). If x
= −6, then y = −6 + 4 = −2, and Quantity B is greater. Eliminate
(C), and select (D).
7. B
Plug in for the radius, n, and solve for x. Let’s make n = 3: The area
of the base of the cylinder is now 9π, and the circumference of the
base is 6π. The ribbon itself is a rectangle, and we now know both
its area, which is the same as the area of the base, and its length,
which is the same as the circumference of the base. Now we can
solve for x, which is the other side of the rectangle: 6πx = 9π, so x
=
, or
. Our value for n is greater than our value for x, so
Quantity B is greater.
8. C
Remember that median is the number that ends up in the middle of
the list when you rewrite the list in numerical order. Find x: The
even numbers are 2, 2, 6, 8. Because 2 and 6 are in the middle, find
their mean:
= 4. So, x = 4. Find y: The prime numbers are 2,
2, 3, 5, 7, 13. Remember: 1 is not prime. Because 3 and 5 are in the
middle, find their mean:
= 4. So, y = 4. Find z: The least is 1,
and the greatest is 15. The median of 1 and 15 is
= 8. So, z =
8. For Quantity A, find the median of 2(4), 4, and 8: So, the median
of 4, 8, 8 is 8. Quantity B is also 8.
9. 1,625
Set up a proportion:
. Cross-multiply to
find that x = 500 × 3.25 = 1,625 gallons.
10. B
Plug In the Answers, starting with the middle choice. If 120 dogs
were sold in March, then 60 cats were sold that month. In April,
240 dogs were sold, along with 180 cats. The total number of dogs
and cats sold during those two months is 600, which is too large, so
eliminate (C), (D), and (E). Try (B). If there were 100 dogs sold in
March, then 50 cats were sold; in April, 200 dogs were sold along
with 150 cats. The correct answer is (B) because 100 + 50 + 200 +
150 = 500.
11. C
Notice that the length of WZ is 4 – (–2) = 6. If area is 18 = 6 × w,
then w is equal to 3. Now you have a right triangle with legs of 3
and 6. Use the Pythagorean theorem: 32 + 62 = c2, or 9 + 36 = c2.
So, c =
=
=3
.
12. E
Order matters in this problem, so remember you do not divide; you
multiply! For the first integer, you have 5 options. For the second,
you have 4. For the third, you have 3; 5 × 4 × 3 is 60, which is (E).
13. D
The percent increase in the CEO’s pay was
× 100% = 900
percent. The percent decrease in the factory workers’ pay was
× 100% = 50 percent. To find what percent greater 900
percent is than 50 percent, do the following:
× 100%
= 1,700 percent, or (D).
14. D
Divide the $9.4 million in private donations received by child
safety organizations in September 1989 by the 38 organizations
operating at the time. The amount is approximately $250,000.
15. C
From the line graph, you see that homeless aid groups took in
about $300 million in private donations, and animal rights groups
about $225 million. The ratio of $300 million to $225 million is 4
to 3.
16. E
Identify the markers for September 1989 and October 1989 on the
chart. The question is asking about the least percent increase
between these two data points. So, begin by evaluating the data
points. All of the differences between the data points for these two
months are very similar; they all seem to have a difference of
approximately 0.5. Because 0.5 is a lesser percent of a greater
number, the least percent increase corresponds to the data point
with the greatest numbers. Therefore, the correct answer is (E),
child safety. Alternatively, find the percent increase for each of the
answer choices by dividing the difference between the two points
by the original, which in this case is the number for September
1989. The least percent increase is still (E), child safety, which is
the correct answer.
17. D
This is a pattern problem. The pattern has five digits: 06539.
Divide 34 by 5, which gives you a remainder of 4. So the 34th digit
will be the fourth in the pattern, which is 3.
18.
First, solve for x using the equation
= 7. Cross-multiply to find
that 7y = 14x. Dividing both sides by 14 yields
y = x. Substitute
this expression into the first equation to get 3( y) + 2y = 24.
Combine the like terms to get y = 24; multiply both sides by
find y =
to
.
19. C
Plug In the Answers, which are the possible values of x. Start with
(C). Find the average of 6, 8, 10, and 23, which is 11.75, which is
in the correct range. Eliminate (A) and (B) because the question
asks for the greatest possible value of x. Next, try (D). The average
of 6, 8, 10, and 28 is 13, which lies outside of the range. The
correct answer is (C).
20. A
Plug In! To find the area of quadrilateral ABDE, find the area of
right ΔABC and subtract the area of right ΔEDC. Make a = 4 and b
= 2. Because AB = BC, we know that this triangle has a height and
base that are both equal to 4. The area of ABC is 4 × 4 ×
area of EDC is 2 × 2 ×
= 8. The
= 2. The area of ABDE is 8 − 2 = 6. Plug
in for a and b and find that (A) is the only one that works.
Alternatively, to find the area of quadrilateral ABDE, find the area
of right ΔABC and subtract the area of right ΔEDC. Both the base
and the height of ΔABC are a, so the area equals
× a × a, or
.
Both the base and the height of ΔEDC are b, so the area equals
×
b × b, or
.
. Therefore, the area of quadrilateral ABDE is
−
Section 6
1. original and outlandish
Try working with the second blank first. The clues are that the
fashions were “considered daring” and then “imitated.” Starting
with the second blank, the sentence suggests that the fashions have
changed from what they once were—in other words, daring.
Outlandish is a good synonym for daring and it makes sense that,
in the first blank, the fashions were original and then lost their
impact because of excess imitation.
2. diverge
Take note of the time transition at one time inseparable…now,
which indicates that the combined roles in Middle Eastern music
are now not inseparable. You need a word that means divide or
separate. Divulge starts with the proper root, but its meaning is way
off. Meanwhile, neither retreat nor retrench means divide, while
fuse is the opposite of what you want. Diverge is the correct
answer.
3. rebuked, perfidy, and expiate
Start with the second blank, which must mean something close to
an act of “treachery.” Perfidy means this. Since his contemporaries
believed Kazan had committed treachery, they would have “harshly
criticized” him, so the first blank means rebuked. For the last
blank, he was able to achieve atonement, which is what expiate
means.
4. soporific
The sentence requires you to figure out the effect that “tranquilizers
usually have,” and this is provided by the clue in the later part of
the sentence, when we read that the “abuse of these drugs results in
a failure to induce the much-desired sleep.” You can infer that the
usual effect of tranquilizers is to produce sleep. Soporific, which
means sleep-inducing, is the correct answer choice. While sedulous
might remind you of “sedative,” it actually means hard-working.
5. preternatural, preclude, and consonant
The clue for the first blank is “are rejected by modern science in its
attempts to find secular insights.” Otherworldly interpretations
contrast the secular, and the best choice for the first blank is
preternatural. There would be a paradox only if scientists could
hold non-secular beliefs. Therefore, a good word for the second
blank is prevent, and a good phrase for the last blank would be in
agreement. Preclude is synonymous with prevent, and consonant is
synonymous with in agreement, making these the correct answers.
6. conformity and eccentricity
Try working with the second blank first. The clue is “none of the
family members were fearful…of appearing or acting differently
from other people.” Therefore, find a word for the second blank
that means uniqueness. Eccentricity fits the bill. Considering the
clue, “The Johnson’s were not known for their,” the two blanks
must be opposites. Eliminate candor and vulgarity based on the
clue and the word choice for the second blank, and choose
conformity.
7. E
In the last paragraph, the author discusses the difficulties inherent
in measuring intergalactic distances. He notes that scientists use a
standard candle in combination with the inverse square law to
measure those distances.
8. C
The passage states in the third paragraph that brighter objects are
closer than dim objects, so eliminate (A). The passage never
specifies what scientists know about the age of astronomical
objects, so eliminate (B). The first paragraph says that, according
to Hubble’s law, “objects farther away from Earth are receding
faster than those closer.” This means that the farther object will
travel faster, so (C) is correct.
9. B
According to the last line in the paragraph, “By the inverse square
law, galaxy B is ten times farther away than galaxy A, assuming, of
course, that distance is the only factor affecting brightness.”
Therefore, if interstellar dust affects the brightness of an object, the
brightness of the object is affected, and the distance scientists
measure may be inaccurate.
10. C
According to the passage, “By the inverse square law, galaxy B is
ten times farther away than galaxy A, assuming, of course, that
distance is the only factor affecting brightness.” Therefore,
assuming that all other factors affecting brightness can be known,
we can conclude that the brighter of the supernovas will be closer
to Earth.
11. B
“Prozac lag” is a phenomenon for which there is currently no
explanation, but neurogenesis may offer a solution. Choice (A)
contradicts this. The passage offers “Prozac lag” as supporting
evidence of a new theory, not disproving an old one, as (C)
suggests, or disproving a new one, as (D) states. Choice (E) goes
too far by discussing “unforeseen effects.” Choice (B) is the best
option.
12.
However, patients suffering from depression only begin to
experience mood elevation weeks after beginning treatment.
The second paragraph has five sentences, so this question has five
answer choices. For an “unexpected observation,” a good place to
start would be to check the transition words. The fourth sentence
starts with the word “however.” While the effects should occur
immediately, these don’t occur until weeks after starting treatment.
The answer is the fourth sentence.
13. edifying and didactic
The blank describes Socrates’s conversations. The clue is
“Socrates’s teachings have survived and continue to enlighten
seekers of wisdom,” so the blank must mean instructional. Edifying
and didactic are the closest in meaning. Tedious, grating, inspiring,
and rousing could all be used to describe Socrates’s conversations,
but they do not match the clue.
14. satiate and allay
You would expect “the colossal meal” to fill someone up, but the
sentence says that “failed to…her voracious appetite.” Thus, she
was not full, and the meal failed to satisfy. Satiate and allay are the
best match. Cadge and mendicate mean the meal begged her
hunger. Exacerbate and provoke go in the wrong direction.
15. iridescent and pavonine
The clue for this sentence is “the lovely rainbows they produce,”
which suggests that the blank should be filled by a word meaning
colorful. Both iridescent and pavonine mean exactly that. Even if
you don’t agree that the blank necessarily refers to rainbows of
color, the missing word does have to agree with beautiful due to the
transition word and, and none of the other four options does:
Anodyne means eliminating physical pain, monocoque means
constructed in one piece, parietal mean college-related, and
saturnine means gloomy.
16. cauterized and inured
The clue for this sentence is callous, so the blank must mean “used
to,” or “didn’t notice.” Choices (B), cauterized, and (E), inured,
mean this. Choice (F) is incorrect because he didn’t notice the
violence more, but rather noticed it less.
17. D
The conclusion of the argument is that the old formula for
Megapower contained natural kiwi extract, while the new formula
does not. The evidence is that Tasmania suffered a decrease in its
kiwi exports. The assumption is that Megapower is not getting kiwi
fruit from Tasmania. Choice (D) strengthens the argument by
pointing out that kiwi imports have fallen in the country that
produces Megapower, which would reinforce that assumption that
the manufacturer is not getting kiwis from Tasmania. Choice (A)
would weaken the argument by providing a potential alternate
source for kiwi fruit. Choice (C) weakens the argument by
providing evidence that the manufacturer of Megapower could be
getting kiwi fruit from another source. Choices (B) and (E) are not
relevant to the conclusion.
18. C
While the word promulgated can take on the meanings given in
(A), (B), or (C), within the context of the sentence it is clear that
Courbet is taking a stand on what he believes art should be.
Therefore, (C) is closest to the correct meaning.
19.
The argument has been made that the painting struck a blow
for the independence of the artist, and that since Courbet’s
work, artists have felt freed from the societal demands placed
upon their work.
While the rest of the passage enumerates Courbet’s ideas on
painting, only this sentence points to the effect that Courbet’s work
may have had on other artists when it states that “since Courbet’s
work artists have felt freed from the societal demands placed on
their work.”
20. A
According to the passage, Courbet broke with convention by
“striving to do something strikingly original.” Only (A) provides
that sense of defying a convention to do something original.
Chapter 20
Practice Test 2
Click here to download a PDF of Practice Test 2.
SECTION 1: ISSUE TOPIC
Directions:
You will be given a brief quotation that states or implies an issue of general interest and specific
instructions on how to respond to that issue. You will have 30 minutes to plan and compose a response
in which you develop a position on the issue according to the specific instructions. A response to any
other issue will receive a score of zero.
“Studying foodways—what foods people eat and how they produce, acquire, prepare, and consume
them—is the best way to gain deep understanding of a culture.”
Write an essay in which you take a position on the statement above. In developing and supporting your
position, you should consider ways in which the statement might or might not hold true.
SECTION 2: ARGUMENT TOPIC
Directions:
You will be given a short passage that presents an argument, or an argument to be completed, and
specific instructions on how to respond to that passage. You will have 30 minutes to plan and compose a
response in which you analyze the passage according to the specific instructions. A response to any
other argument will receive a score of zero.
Note that you are NOT being asked to present your own views on the subject. Make sure that you
respond to the specific instructions and support your analysis with relevant reasons and/or examples.
Fossil evidence indicates that the blompus—an extremely large, carnivorous land mammal—
inhabited the continent of Pentagoria for tens of thousands of years until its sudden decline and
ultimate extinction about twelve thousand years ago. Scientists have determined that the extinction
coincided with a period of significant climate change and with the arrival of the first humans. Some
scholars theorize that the climate change so altered the distribution of plants and animals in the
environment that the food chain upon which the blompus depended was irretrievably disrupted.
Others contend that predation by humans is the more plausible explanation for the rapid population
decline.
Write a response in which you discuss specific evidence that could be used to decide between the
proposed explanations above.
SECTION 3: VERBAL REASONING
For questions 1 through 6, select one entry for each blank from the corresponding column of choices.
Fill all blanks in the way that best completes the text.
1 of 20
The (i)____________with which a statement is conveyed is frequently more important to the listener in
determining the intended meaning than the actual words (ii)____________. For example, a compliment,
when delivered sarcastically, will be perceived by the receiver as fairly insulting.
2 of 20
Though a film studio produces works that are (i)____________and artistic, its priorities often dictate
that creativity be (ii)____________to a secondary position since the creative process can
(iii)____________the organization and hierarchy necessary to running a large company.
3 of 20
Science and religion each have core tenets that are considered ____________; however, because some
scientific tenets are in conflict with some religious ones, these tenets cannot all be correct.
4 of 20
Although most preventative medical ointments commonly in use would have (i)____________ an
infection, the particular one Helen applied to her sores actually, much to her dismay,
(ii)____________her (iii)____________.
5 of 20
A single (i)____________remark can easily ruin the career of a politician, so most are trained to avoid
such offhand remarks and instead stick to prepared talking points. This training can result in a lack of
(ii)_______, however, and elicit merely (iii)_____, lukewarm responses from crowds.
6 of 20
Oscar Wilde’s The Importance of Being Earnest satirizes the ____________nature of upper crust British
society; its characters take trivial concerns seriously while thoughtlessly dismissing important ones.
For each of Questions 7 to 12, select one answer choice unless otherwise instructed.
Questions 7 through 10 are based on the following reading passage.
In 1798, economist Thomas Robert Malthus stated in his “Essay on the Principle of Population”
that “population increases in a geometric ratio, while the means of subsistence increases in an arithmetic
ratio.” However, Malthus’s dire prediction of a precipitous decline in the world’s population has not
come to pass. The miscalculations in what has come to be known as the Malthus Doctrine are partly due
to Malthus’s inability to foresee the innovations that allowed vast increases in worldwide wheat
production.
In the late nineteenth century, the invention of the tractor staved off a Malthusian disaster. While
the first tractors were not particularly powerful, the replacement of animals by machinery meant that
land that had been devoted to hay and oats could now be reclaimed for growth of crops for human
consumption. Nevertheless, the Malthusian limit might still have been reached if crop yield had not
been increased.
A natural way to increase crop yield is to supply the soil with additional nitrogen. In 1909, chemist
Fritz Haber succeeded in combining nitrogen and hydrogen to make ammonia, the white powder
version of which, when added to the soil, improves wheat production. Haber nitrogen, however, was not
widely used until later in the twentieth century, largely due to farmers’ resistance to spreading an
unnatural substance on their crops. Haber’s invention had a further drawback: If applied in incorrect
quantities, the wheat crop would grow taller and thicker, eventually toppling over and rotting.
Interestingly, in the late twentieth century the discovery of genetic engineering, which provides a
means of increasing rice and maize production, met with equal resistance, this time from the
environmental movement. Even without direct genetic engineering, it is likely that science will discover
new methods to improve agricultural production.
7 of 20
According to the passage, which of the following is true about Haber nitrogen?
Haber nitrogen is more effective at increasing the yield of wheat crops than that of maize or oat
crops.
Undesired effects can result from the application of surplus quantities of Haber nitrogen.
Haber nitrogen was the first non-naturally occurring substance to be applied to crops as
fertilizer.
Haber nitrogen may not be effective if applied at an improper time in wheat’s growth cycle.
Farmers were quick to adopt Haber nitrogen because it made their crops grow taller and thicker.
8 of 20
The passage implies all of the following EXCEPT
world food production has kept pace with world population growth
technological innovation is one factor that allowed for an increase in crop production
farmers are not the only group that has opposed artificial efforts to increase crop yield.
the Malthusian limit might well have been reached if new methods to increase crop production
had not been found
a Malthusian disaster would have been ensured if it were not for the invention of genetic
engineering
9 of 20
Which of the following, if true, would best represent Malthus’ contention in the first paragraph?
By 2040 the world’s population increases marginally, and food production keeps pace with
demand.
By 2040 the world’s population decreases marginally, and food production outstrips demand.
By 2040 the world’s population remains unchanged, and food production declines slightly.
By 2040 the world’s population has significantly increased, and food production has increased
slightly.
By 2040 the world’s population has significantly decreased, and food production has decreased
slightly.
10 of 20
Which of the following most nearly means the word precipitous, as used in context?
anticipated
deliberate
gradual
risky
sharp
Questions 11 through 12 are based on the following reading passage.
The dearth of natural resources on the Australian continent is a problem with which government
officials there have long struggled. As long distance travel has become less of an obstacle, the tourism
industry has become ever more important to the national economy. Tourism represents more than 10
percent of national export earnings annually, and in less developed regions such as the Western
Territory, the percentage is much higher.
Unfortunately, this otherwise rosy prospect has one significant cloud on the horizon. In recent
years, there has been a move towards returning some of the land to the Aboriginal people. As Western
society and culture have flourished on Australian soil, tribal people have been forced ever farther inland
in an attempt to maintain their traditional ways of living, a desire that the government has striven to
respect.
One of the central beliefs of the Aboriginal religion is that certain natural formations have spiritual
significance and must be treated accordingly. Strict guidelines determine who may visit these sites and
at what times. Unfortunately, many of these sites are the very natural wonders tourists flock to see. If
non-Aboriginal people are forbidden to visit these natural wonders, many may choose not to vacation in
a region that sorely needs the income generated by tourism.
The Australian government has dealt with this dilemma thus far by trying to support both sides.
The Aboriginal council is still trying to put an end to such use of certain sites, however, and it remains
to be seen whether respect for tradition or economic desires will ultimately triumph.
11 of 20
In the context of the passage, which of the following most closely matches the meaning of the phrase
“otherwise rosy prospect has one significant cloud on the horizon”?
A colorful sunset is marred by a dark storm cloud.
A generally promising future has a potential problem.
The view is beautiful but partially blocked.
The future of the Aboriginal people is doubtful.
Although the situation looks good, in reality it is hopeless.
12 of 20 Consider each of the choices separately and select all that apply.
According to the passage, which of the following is a cause of the current dispute between the
Aborigines and the Australian government?
economic hardships in certain regions of the country
increasing dominance by European norms and lifestyles
limited natural resources in most of Australia
For questions 13 through 16, select the two answer choices that, when used to complete the sentence, fit
the meaning of the sentence as a whole and produce completed sentences that are alike in meaning.
13 of 20
George was a mercurial character; one moment he was optimistic about his prospects, and the next he
was ____________.
immoral
hopeful
witty
morose
dour
buoyant
14 of 20
Growing up in a wealthy suburb, she felt quite the ____________as she began her first job as a llama
caretaker on a rural farm.
tyro
concierge
agronomist
cultivator
neophyte
curator
15 of 20
William Shakespeare’s Macbeth was based upon a highly ____________version of events that the
playwright wrought from Raphael Holinshed’s Chronicles of England, Scotland, and Ireland; King
Duncan’s death at the hand of Macbeth comprises the play’s only historical truth.
anachronistic
effusive
embellished
prosaic
serpentine
colored
16 of 20
While comic book artists such as Neal Adams demonstrated a more thorough mastery of human
anatomy than did the generation that preceded them, some readers wondered whether the superheroes
they drew were really supposed to be so ____________ that every detail of their musculatures would be
visible through their clothing.
thewy
sinewy
superfluous
pneumatic
flocculent
atrophied
For each of Questions 17 to 20, select one answer choice unless otherwise instructed.
Questions 17 through 18 are based on the following reading passage.
One of the most curious structures in cellular biology is the telomere, a length of repeated bases
located at the end of every chromosome that, unlike the rest of the DNA strand, carries no useful genetic
information. While the telomere seems on the surface to be nothing more than a useless afterthought of
DNA, a closer look proves that it is not only important, but also crucial to the functioning of any
organism. Indeed, without this mundane structure, every cell division would be a step into senescence,
and the onset of old age would begin at birth.
Scientists have found that during cell division not every base of the DNA strand can be replicated,
and many, especially those near the end, are lost. If, instead of telomeres, our chromosomes stored
valuable genetic information at the end of the DNA strand, then cell division would cause our cells to
lose the ability to code for certain information. In fact, many ailments associated with normal old age
begin only after the telomere buffer has been exhausted through years of cell division.
17 of 20
Consider each of the choices separately and select all that apply.
Which of the following can reasonably be inferred based on the passage?
An individual who aged faster than the average person may have had a shorter telomere buffer
than the average person.
Scientists once believed that telomeres served no useful purpose.
If DNA degradation were absent, then telomeres would be less important to human health.
18 of 20
The passage suggests that if telomere buffers did not exist
problems associated with aging would begin earlier in life
people would age so rapidly that almost no one would live past childhood
cellular senescence would probably be prevented by DNA bases
chromosomes would lose the ability to store genetic codes
DNA strands would contain only useful genetic information
Questions 19 through 20 are based on the following reading passage.
Music education in America emerged in the early eighteenth century out of a desire to ensure that
church goers could sing the weekly hymns in tune. In 1721, John Tufts, a minister, penned the first
textbook for musical education entitled An Introduction to the Singing of Psalm Tunes. Tufts’s
pedagogical technique relied primarily on rote learning, omitting the reading of music until a student’s
singing abilities had improved.
In the same year that Tufts’s publication emerged, Reverend Thomas Walter published The
Ground and Rules of Music Explained, which, while also focusing on preparing students to sing
religious music, took a note-based approach by teaching students the rudiments of note reading from the
onset. The “note versus rote” controversy in music education continued well into the mid-nineteenth
century. With no curriculum to guide them, singing school teachers focused on either the rote or note
method with little consistency.
19 of 20
The author discusses Walter’s pedagogical technique in order to
suggest that rote learning is superior to note learning
present a contrast with Tufts’s educational technique
argue that rote learning improves a student’s singing ability
show the origin of Tufts’s educational techniques
show that rote learning was inconsistently practiced
20 of 20
Select the sentence in the passage that best describes the endurance of the tension between pedagogical
techniques.
SECTION 4: QUANTITATIVE REASONING
For each of Questions 1 to 8, compare Quantity A and Quantity B, using additional information
centered above the two quantities if such information is given. Select one of the four answer choices
below each question and fill in the circle to the left of that answer choice.
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
A symbol that appears more than once in a question has the same meaning throughout the question.
1 of 20
Quantity A
Quantity B
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
2 of 20
5 is r percent of 25.
s is 25 percent of 60.
Quantity A
Quantity B
r
s
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
3 of 20
g and h are positive integers such that the value of g is twice the value of h.
Quantity A
Quantity B
The ratio of g to 1 The ratio of 1 to h
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
4 of 20
Quantity A
Quantity B
The average (arithmetic mean)
of 67, 78, x, and 101
The average (arithmetic mean)
of 66, 79, x, and 102
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
5 of 20
In a certain country the total weight of recycled newspapers increases annually by 0.79 million tons.
Quantity A
Quantity B
The percent increase in the
weight of recycled newspapers
in 1989 over 1988
The percent increase in the
weight of recycled newspapers
in 1990 over 1989
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
6 of 20
Quantity A
Quantity B
The total weight of m peanuts
with a weight of n + 3 mg each
The total weight of n almonds
with a weight of m + 3 mg
each
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
7 of 20
Quantity A
Quantity B
527(575)
528(115)
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
8 of 20
Alejandro has a six-sided die with faces numbered 1 through 6. He rolls the die twice.
Quantity A
The probability that he rolls
two even numbers
Quantity B
The probability that neither
number rolled is a multiple of
3
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
9 of 20
If 4(r – s) = −2, then what is r, in terms of s ?
s+2
2s
10 of 20
At Tenderloin Pharmaceuticals, 25 percent of the employees take the subway to work. Among those
who ride the subway, 42 percent transfer from one subway line to another during their commutes, and
the rest do not transfer. What percent of all employees transfer lines?
11 of 20
If the value of the expression above is to be halved by doubling exactly one of a, b, c, d, or e, which
should be doubled?
a
b
c
d
e
12 of 20
=
2−2
2−
8 −2
2
8 −2
13 of 20
ΔABC has an area of 108 cm2. If both x and y are integers, which of the following could be the value of
x?
Indicate all such values.
4
5
6
8
9
14 of 20
In Year x, on which other continent did electricity production most closely equal electricity production
in Europe?
Africa
Asia
Australia
South America
North America
15 of 20
In Year x, for which continent was the ratio of electricity production to percent of population the
greatest?
Africa
Asia
South America
Europe
North America
16 of 20
In Year x, if South America had a population of approximately 368 million, what was the approximate
population, in millions, of Africa?
494
470
274
150
39
17 of 20
The average (arithmetic mean) weight of 5 crates is 250 pounds. The 2 lightest crates weigh between
200 and 205 pounds each, inclusive, and the 2 heaviest crates weigh between 300 and 310 pounds each,
inclusive. If the weight of the fifth crate is x pounds, then x is expressed by which of the following?
220 ≤ x ≤ 250
230 ≤ x ≤ 260
240 ≤ x ≤ 270
250 ≤ x ≤ 270
260 ≤ x ≤ 280
18 of 20
In a certain sequence, s1, s2…sx if s1 = 2, s2 = 2, s3 = 2, and for x ≥ 4, sx = 2sx –1 + sx − 2, what is the
value of s6 ?
30
34
37
38
40
19 of 20
Y is a point on line segment XZ such that XY = XZ. If the length of YZ is 4a + 6, and the length of XZ is
68, then a =
20 of 20
Talk show host Ralph Burke has exactly one guest on his show each day, and Burke’s show airs every
Monday through Friday. Burke always schedules politicians on Mondays and Wednesdays, actors on
Tuesdays and athletes on Thursdays, but can have a guest of any one of these three kinds on Friday. No
guest appears more than once per week on Burke’s show. If Burke has five politicians, three actors and
six athletes he could invite, and if no politician is also an actor or an athlete and no actor is also an
athlete, how many different schedules of guests from Monday to Friday could Burke create?
30
1,200
3,600
4,500
6,300
SECTION 5: VERBAL REASONING
For questions 1 through 6, select one entry for each blank from the corresponding column of choices.
Fill all blanks in the way that best completes the text.
1 of 20
Despite what ____________philosophies of child-rearing suggest, there is no imperative that the dayto-day action of raising a child be simple, unambiguous, and unchanging—no requirement, in other
words, ensures that life follows philosophy.
2 of 20
All the greatest chess players in the world know that it is folly to be (i)____________ when facing a
formidable opponent, as stubbornness will almost surely lead to mistakes that force a player to
(ii)____________ to the prevailing strategy of his or her opponent.
3 of 20
The novel emphasizes the innate (i)____________ of all humans, showing how each and every
character within the narrative is, ultimately, (ii)____________ . This motif becomes tiresome due to its
(iii)____________, however, as character after character is bribed, either explicitly or implicitly, into
giving up his or her supposedly cherished beliefs.
4 of 20
Although pirating software, such as borrowing a friend’s copy of an installation CD or downloading
software from unapproved sources is (i)____________, many people continue to do so
(ii)____________, almost as if they were unaware that such acts amount to theft.
5 of 20
Having squandered his life’s savings on unprofitable business ventures, the ____________entrepreneur
was forced to live in squalor.
6 of 20
Teachers of composition urge their students to (i)____________in their writing and instead use clear,
simple language. Why use a (ii)___________ vocabulary when (iii)____________phrasing conveys
one’s meaning so much more effectively?
For each of Questions 7 to 11, select one answer choice unless otherwise instructed.
Questions 7 through 8 are based on the following reading passage.
Neurobiologists have never questioned that axon malfunction plays a role in neurological
disorders, but the nature of the relationship has been a matter of speculation. George Bartzokis’s
neurological research at UCLA suggests that many previously poorly understood disorders such as
Alzheimer’s disease may be explained by examining the role of the chemical compound myelin.
Myelin is produced by oligodendrocyte cells as a protective sheathing for axons within the
nervous system. As humans mature and their neurochemistries grow more complex, oligodendrocyte
cells produce increasing amounts of myelin to protect the byzantine circuitry inside our nervous
systems. An apt comparison may be to the plastic insulation around copper wires. Bereft of myelin,
certain areas of the brain may be left vulnerable to short circuiting, resulting in such disorders as
ADHD, schizophrenia, and autism.
7 of 20
Consider each of the choices separately and select all that apply.
It can be inferred from the passage that the author would be most likely to agree with which of the
following statements regarding the role of myelin?
The levels of myelin in the brain can contribute to the neurological health of individuals.
Increasing the levels of myelin in the brain can reverse the effects of neurological damage.
The levels of myelin in the brain are not fixed throughout the lifetime of an individual.
8 of 20
In the context in which it appears, byzantine most nearly means
devious
intricate
mature
beautiful
electronic
9 of 20
The cost of operating many small college administrative offices is significantly reduced when the
college replaces its heavily compensated administrative assistants with part-time work-study students
whose earnings are partially subsidized by the government. Therefore, large universities should follow
suit, as they will see greater financial benefits than do small colleges.
In the above argument it is assumed that
replacing administrative assistants with work-study students is more cost-effective for small
colleges than for large universities
large universities usually depend upon small colleges for development of money-saving
strategies
the financial gains realized by large universities would not be as great were they to use nonwork-study students in place of the administrative assistants
work-study students at large universities could feasibly fulfill a similar or greater proportion
of administrative assistant jobs than what they could at small colleges
the smaller the college or university, the easier it is for that college or university to control
costs
Questions 10 through 11 are based on the following reading passage.
The nineteenth century marked a revolutionary change in the way wealth was perceived in
England. As landed wealth gave way to monied wealth, investments became increasingly speculative.
A popular investment vehicle was the three-percent consol which took its name from the fact that
it paid three pounds on a hundred pound investment. The drawback to the consol was that once issued,
there was no easy way for the government to buy back the debt. To address the problem, the British
government instituted a sinking fund, using tax revenue to buy back the bonds in the open market. The
fact that the consol had no fixed maturity date ensured that any change in interest rate was fully
reflected in the capital value of the bond. The often wild fluctuation of interest rates ensured the
consol’s popularity with speculative traders.
10 of 20
Which of the following best describes the relationship of the first paragraph of the passage to the
passage as a whole?
It provides a generalization which is later supported in the passage.
It provides an antithesis to the author’s main argument.
It briefly compares two different investment strategies.
It explains an investment vehicle that is later examined in greater detail.
It provides a historical framework by which the nature of the nineteenth-century investor can
more easily be understood.
11 of 20
In the second paragraph, select the sentence that describes a solution to a problem.
For questions 12 through 15, select the two answer choices that, when used to complete the sentence, fit
the meaning of the sentence as a whole and produce completed sentences that are alike in meaning.
12 of 20
Owing to a combination of its proximity and ____________atmosphere, Mars is the only planet in our
solar system whose surface details can be discerned from Earth.
viscous
ossified
rarefied
estimable
copious
meager
13 of 20
Using the hardships of the Joad family as a model, John Steinbeck’s The Grapes of Wrath effectively
demonstrated how one clan’s struggles epitomized the ____________experienced by an entire country.
reticence
adversity
repudiation
quiescence
verisimilitude
tribulation
14 of 20
The Mayan pyramid of Kukulkan is more than just ____________edifice; this imposing structure was
built to create a chirping echo whenever people clap their hands on the staircase. This echo sounds just
like the chirp of the Quetzal, a bird which is sacred in the Mayan culture.
a venerable
a humble
a beguiling
an august
a specious
a prosaic
15 of 20
Some wealthy city-dwellers become enchanted with the prospect of trading their hectic schedules for a
bucolic life in the countryside, and they buy property with a pleasant view of farmland—only to find the
stench of the livestock so ____________that they move back to the city.
bovine
pastoral
noisome
atavistic
olfactory
mephitic
For each of Questions 16 to 20, select one answer choice unless otherwise instructed.
Questions 16 through 18 are based on the following reading passage.
Often the most influential developments initially appear to be of minor significance. Consider the
development of the basic stirrup for example. Without stirrups horse and rider are, in terms of force,
separate entities; lances can be used from horseback, but only by throwing or stabbing, and mounted
warriors gain only height and mobility. In medieval times, a lance couched under the rider’s arm,
unifying the force of rider and weapon, would throw its wielder backwards off the horse at impact.
Stirrups unify lance, rider, and horse into a force capable of unprecedented violence. This development
left unusually clear archaeological markers: With lethality assured, lances evolved barbs meant to slow
progress after impact, lest the weight of body pull rider from horse. The change presaged the dominance
of mounted combat, and increasingly expensive equipment destroyed the venerable ideal of freeman
warriors. New technology demanded military aristocracy, and chivalric culture bore its marks for a
millennium.
16 of 20
The primary purpose of the passage is to
discuss the influence of a recent archeological discovery
explore the societal significance of a technological innovation
assess the state of research in a given field
lament the destruction of certain social ideals
explicate the physics of combat artillery
17 of 20
It can be inferred from the passage that the author believes which of the following about innovations in
military technology?
Their study merits additional research.
They had more lasting influence than did those of the ancient world.
Most of them had equally far-reaching repercussions.
Prior to their application, the military value of horses was considered insignificant.
Many of them are archaeologically ambiguous.
18 of 20
Select the sentence in the passage in which the author cites the physical effects of a technological
innovation being discussed as an example of a previous generalization.
Questions 19 through 20 are based on the following reading passage.
Few mathematical constructs seem as conceptually simple as that of randomness. According to the
traditional definition, a number is random if it is chosen purely as the result of a probabilistic
mechanism such as the roll of a fair die. In their groundbreaking work regarding complexity and the
limitations of formal systems, mathematicians Gregory Chaitin and A.N. Kolmogorov force us to
consider this last claim more closely.
Consider two possible outcomes of throwing a fair die three times: first, 1, 6, and 2; second 3, 3, and 3.
Now let us construct two three-member sets based on the results. Though the first set—{1,6,2}—
intuitively seems more random than the second—{3,3,3}, they are each as likely to occur, and thus
according to the accepted definition, must be considered equally random. This unwelcome result
prompts Chaitin and Kolmogorov to suggest the need for a new standard of randomness, one that relies
on the internal coherence of the set as opposed to its origin.
19 of 20
Which of the following best describes the organization of the passage as whole?
A concept is introduced; a traditional definition is put forward; a thought experiment is
described; a new definition is proposed; the traditional definition is amended as a result.
A concept is introduced; a traditional definition is supported by authorities; a thought
experiment is described; the implications of the experiment are discussed.
A concept is introduced; a traditional definition is considered and rejected; a thought
experiment is described; a new definition is proposed.
A concept is introduced; a traditional definition is called into question; a thought experiment is
described; the implications of the experiment are discussed.
A concept is introduced; authorities are called in to reevaluate a definition; a thought
experiment is described; the implications of the experiment are considered and rejected.
20 of 20
Consider each of the choices separately and select all that apply.
Which of the following is an inference made in the passage above?
The results of the same probabilistic mechanism will each be as likely as the other to occur.
According to the traditional definition of randomness, two numbers should be considered
equally random if they result from the same probabilistic mechanism.
Different probabilistic mechanisms are likely to result in similar outcomes.
SECTION 6: QUANTITATIVE REASONING
For each of Questions 1 to 7, compare Quantity A and Quantity B, using additional information centered
above the two quantities if such information is given. Select one of the four answer choices below each
question and fill in the circle to the left of that answer choice.
(A) Quantity A is greater.
(A) Quantity B is greater.
(A) The two quantities are equal.
(A) The relationship cannot be determined from the information given.
A symbol that appears more than once in a question has the same meaning throughout the question.
1 of 20
Quantity A
Quantity B
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
2 of 20
Quantity A
Quantity B
The distance that Bob drives in
3 hours at an average speed of
44 miles per hour
The distance that Inez drives in
2 hours and 30 minutes at an
average speed of 50 miles per
hour
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
3 of 20
The height of a rectangular solid is increased by p percent, its depth is decreased by p percent and its
width is unchanged.
Quantity A
The volume of the new
rectangular solid if p = 20
Quantity B
The volume of the new
rectangular solid if p = 40
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
4 of 20
In ΔABC, AB = AC
Quantity A
Quantity B
The sum of the degree
measures of angle B and angle
C
90
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
5 of 20
12.5 percent of k is 80. k is y percent of 80.
Quantity A
Quantity B
y
650
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
6 of 20
Set P = {a, b, c, d, e, f, g}
Set Q = {a, b, c, d, e, f}
a, b, c, d, e, f, and g are distinct integers
Quantity A
Range of Set P
Quantity B
Range of Set Q
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
7 of 20
Sequence F is defined as Fn = F(n − 1) + 3 and F1 = 10.
Quantity A
The sum of F4 through F10
Quantity B
The sum of F6 through F11
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
8 of 20
A number, n, is multiplied by 6 and the product is increased by 24. Finally, the entire quantity is divided
by 3. Which of the following is an expression for these operations, in terms of n ?
2n + 8
3n + 24
16n
9 of 20
The average (arithmetic mean) of a and b is 10, and the average of c and d is 7. If the average of a, b,
and c is 8, what is the value of d ?
10 of 20
In the xy-plane, square ABCD has vertices at A (3, 7), B (3, 12), C (8, x), D (8, y). What is the area of
ABCD ?
16
20
25
30
36
11 of 20
Houses Sold in July
Week
Peter
Dylan
Week 1
4
9
Week 2
6
3
Week 3
10
10
Week 4
4
2
The table above shows the number of houses sold per week for the month of July by two real estate
agents, Peter and Dylan. What is the difference between the median number of houses sold per week by
Dylan and the median number of houses sold per week by Peter?
0
1
2
5
6
12 of 20
At Flo’s Pancake House, pancakes can be ordered with any of six possible toppings. If no toppings are
repeated, how many different ways are there to order pancakes with three toppings?
20
40
54
120
720
13 of 20
The area of triangle KLM is equal to the area of rectangle ABCD. If the perimeter of ABCD is 16, what
is the length of LM ?
3
5
6
Questions 14 through 16 refer to the following graph.
14 of 20
For how many of the years shown did the ratings for Program y increase over the ratings for Program y
in the previous year?
Two
Three
Four
Five
Six
15 of 20
In 1995, there were 95 million television households in the United States. In 1983, if the number of
television households was 80 percent of the number of television households in 1995, then
approximately how many television households, in millions, viewed Program y in 1983 ?
80
76
15
12
10
16 of 20
If there were 20 million television households in the United States in 1983, then the number of viewers
of Program x is how much greater than the number of viewers of Program y in 1983 ?
17 of 20
Each of the 576 houses in Tenantville is owned by one of the following landlords: Matt, Gavin, Angela,
or Susan. Matt and Angela together own twice as many houses as Gavin and Susan own. If Gavin owns
100 more houses than Susan owns, and Matt owns 100 more houses than Angela owns, how many
houses does Susan own?
46
142
146
192
242
18 of 20
One-fourth of the cars that an automobile manufacturer produces are sports cars, and the rest are sedans.
If one-fifth of the cars that the manufacturer produces are red and one-third of the sports cars are red,
then what fraction of the sedans is red?
19 of 20
A candy jar has 4 lime, 10 cherry, 8 orange, and x grape candies. If Tom selects a candy from the jar at
random and the probability that he selects an orange candy is greater than 20 percent, which of the
following could be the value of x ?
Indicate all such values.
10
14
18
22
24
28
20 of 20
Square ABCD and a circle with center C intersect as shown. If point E is the center of ABCD and if the
radius of circle C is k, then what is the area of ABCD, in terms of k ?
πk2
k2
2k2
Chapter 21
Practice Test 2: Answers and
Explanations
INTERPRETING YOUR RESULTS
After you check your answers on the following pages, fill out this sheet to
interpret your results.
Analytical Writing
To evaluate your performance on the Analytical Writing sections, compare
your response to the advice and samples in the Analytical Writing chapter.
Verbal Reasoning
Refer to the explanations to check your answers. Count the number of
questions you got correct in each Verbal Reasoning section, and calculate the
total number correct. Find the section of the Interpretive Guide (below) that
corresponds to your total to get an idea of how your performance compares to
that of other test takers.
Test 2
Section 3
Section 5
Total
Quantitative Reasoning
# Correct
Refer to the explanations to check your answers. Count the number of
questions you got correct in each Quantitative Reasoning section, and
calculate the total number correct. Find the section of the Interpretive Guide
(below) that corresponds to your total to get an idea of how your performance
compares to that of other test takers.
Test 2
# Correct
Section 4
Section 6
Total
Interpretive Guide
The table below provides a guide for interpreting your performance based on
the number of questions you got correct in each subject.
Section 3
1. inflection and utilized
For the first blank, the transition “more important” tells you to
change direction from “actual words.” Also, sarcastically is an
example of tone. Look for a choice that means tone. Inflection fits
tone. Pitch is nonverbal, but it does not match the example of
sarcastically. Accuracy does not fit. For the second blank, look for
a word that means conveyed or spoken. Utilized is the best match.
Implied and repudiated don’t fit.
2. expressive, relegated, and conflict with
Try working with the first blank first. The clue is artistic, and the
transition and indicates the first blank should be a word that is the
same as artistic. Expressive is the best choice; neither tedious nor
tiresome works. Though changes the direction of the sentence—
though the studio likes the creative/artistic aspect, something
negative must be happening to creativity—it’s brought down to a
secondary position. Eliminate uplifted and compared for blank (ii)
because they are not negative, and choose relegated. Turning to the
third blank, “organization and hierarchy” are in opposition to
creativity, so conflict with makes the most sense.
3. axiomatic
You are given the clue that the beliefs “are in conflict” and “cannot
all be correct.” Therefore, whatever goes into the blank must be
synonymous with correct or something we can infer correctness
from. The correct answer is axiomatic, which means self-evident or
universally true. Disputable is the opposite of what the sentence
requires, and ubiquitous and historic are not synonymous with selfevident. Although empirical, meaning derived from observation,
might fit science, it is not a good fit for religion.
4. staved off, contributed to, and affliction
The clue “Although most preventative medical ointments
commonly in use” tells you that most ointments would prevent an
infection, but the one Helen used did not. Recycle the clue, and put
a word that means prevent in the first blank; staved off is the best
match. Work with the second and third blanks together. The
ointment did not prevent an infection, and the clue “much to her
dismay” tells you that something bad happened. The only pair that
makes sense together is contributed to and affliction because they
tell you that the ointment made her problem worse.
5. glib, spontaneity, and tepid
For the first blank, the clue is offhand remarks, so the blank means
something like “offhand.” Glib, which means “superficial or
showing a lack of concern,” is the closest match for this. Sticking
to prepared talking points can result in a lack of “excitement” or
“naturalness,” which spontaneity matches. For the last blank, you
know the crowd’s responses are lukewarm, so the answer for that
blank is tepid.
6. shallow
The clue is the entire clause that follows the semicolon: “its
characters take trivial concerns seriously while thoughtlessly
dismissing important ones.” Look for a word that means superficial
or petty to go in the blank. The only one that fits is shallow.
7. B
The third paragraph states that if incorrect quantities of Haber
nitrogen were applied, “the wheat crop would grow taller and
thicker, eventually toppling over and rotting.” Losing a crop would
be an undesirable effect, making (B) the correct answer. Eliminate
(A) because the passage doesn’t compare the effects of Haber
nitrogen on different kinds of crops. The passage doesn’t provide
any information to support (C) and (D). Choice (E) contradicts the
passage, which says the farmers were wary of the substance.
8. E
According to the first paragraph, there has been no sharp decline in
the world’s population and, therefore, we can surmise that food
production has been sufficient to allow for the existing population
growth, as in (A). In the second paragraph, the author mentions the
invention of the tractor as one of the factors that allowed more
crops to be grown for human consumption. This reflects the
technological innovation in (B). In the last paragraph, the author
notes that the environmental movement has opposed efforts at
genetic engineering. Thus, (C) is implied as well. The author notes
that increases in crop production through the invention of the
tractor and ammonia prevented Malthus’s predictions from being
realized, and this rules out (D). The extent of the impact of genetic
engineering is not clear. We don’t know that a Malthusian disaster
would have been a certainty without genetic engineering.
Therefore, the correct answer is (E) because it is not implied.
9. D
The first paragraph states that Malthus believed that “population
increases in a geometric ratio, while the means of subsistence
increases in an arithmetic ratio.” More simply put, Malthus argued
that population growth happens at a significantly faster rate than
food production. Only (D) demonstrates this.
10. E
The first paragraph presents Malthus’s prediction about what would
happen if population growth were to outstrip food production. If
there were too many people and not enough food, you would
expect a significant or rapid population decline. Look for a word to
replace precipitous that is similar to significant or rapid. Sharp,
(E), is the best word.
11. B
The “rosy prospect” refers to the previous paragraph’s discussion
of the booming tourism industry in Australia, which implies a
positive future, and the “cloud on the horizon” refers to the conflict
between the rights of the Aborigines and the need for the money
from tourism, a potential problem. Choice (A) incorrectly interprets
the quote as referring to a literal horizon and prospect. Choice (C)
is also too literal, taking prospect to mean view. Choice (D) is
incorrect because, although this may be true based on later
information in the passage, it is not an accurate interpretation of
this phrase. Choice (E) is too strong because the future is described
as generally good, not hopeless.
12. A, B, and C
All three statements are given as sources of the conflict. Choice
(A), economic hardships, is mentioned in the third paragraph. Due
to financial difficulties, many regions are unwilling to give up the
income derived from tourists visiting Aboriginal lands. Choice (B)
is discussed in the second paragraph. The expansion of Western
culture is the reason that the Aborigines have moved inland and
abandoned other sacred sites. Choice (C) is mentioned in the first
sentence. Tourism is described as particularly important due to the
“dearth of natural resources.”
13. morose and dour
The first part of the clue is “mercurial character,” which means
George’s moods change frequently. The second part of the clue is
“one moment he was optimistic about his prospects,” and the
transition is the next he was. Thus, the blank should be the opposite
of optimistic; look for words that mean pessimistic. Morose and
dour are both similar to pessimistic. Hopeful and buoyant have the
opposite meaning, and witty and immoral are not related.
14. tyro and neophyte
The clue is that she “began her first job.” Also, the contrast of
“wealthy suburb” and “llama caretaker on a rural farm” suggests
that she’d feel out of place or lacking in experience at her first job.
Look for words that mean beginner. Tyro and neophyte are the only
words that mean beginner. Agronomist and cultivator are traps for
people who focused too heavily on the farm. Concierge and
curator are traps for people who focused too heavily on caretaker.
15. embellished and colored
The clue “King Duncan’s death at the hand of Macbeth comprises
the play’s only historical truth” tells you that the version of events
related in Macbeth was not very accurate. Does anachronistic
mean inaccurate? No; cross it out. What about effusive? No. In
contrast, embellished works well, but prosaic and serpentine do
not. Finally, colored—which, like embellished, means
misrepresented or distorted—fits the blank nicely.
16. thewy and sinewy
The word that goes into the blank describes superheroes, of whom
the clue phrase states that “every detail of their musculatures would
be visible through their clothing.” Clearly, something like muscular
is called for, and both thewy and sinewy fit the bill. The other four
words don’t fit: Superfluous means unnecessary, pneumatic means
full of air, flocculent means covered in wool, and atrophied means
shriveled due to disuse.
17. A and C
Choice (A) is correct because the passage states that “…without
this mundane structure, every cell division would be a step into
senescence, and the onset of old age would begin at birth.” Choice
(B) is not correct because we have no information about what
scientists used to think about telomeres. Choice (C) is correct
because we are told that one function of telomeres is to mitigate the
loss of DNA bases. If no bases are lost, then this role is not
important any more.
18. A
The first paragraph says that without telomere buffers “every cell
division would be a step into senescence, and the onset of old age
would begin at birth,” and the last sentence of the passage states
that “many ailments associated with normal old age begin only
after the telomere buffer has been exhausted through years of cell
division.” If the protection offered by the buffers didn’t exist, you
could expect problems related to aging to start sooner, as (A)
suggests. Choice (B) goes too far; though the passage speaks on the
onset of old age at birth, we can’t be sure that almost no one would
live past childhood. The passage provides no support for (C), (D),
or (E).
19. B
The passage as a whole provides a short history of two types of
early musical education, the rote method and the note method.
Nowhere in the passage does the author come out in favor of either
method, thereby ruling out (A) and (C). Given that Reverend
Walter taught music by the note method he developed, (D) doesn’t
make sense. While it is true that rote learning was inconsistently
practiced, as (E) states, this does not answer the question.
20.
The “note versus rote” controversy in music education
continued well into the mid-nineteenth century.
The use of the word “controversy” in the final paragraph is the only
indication the author gives that the decision between “note” or
“rote” as a musical learning technique was in any way contentious.
Section 4
1. C
The Quantities have numbers with great exponents and none of the
exponent rules can be applied, so look for a way to factor. In
Quantity A, factor 987 into its prime factors. The prime factors of
98 are 2 × 7 × 7, so 987 can be rewritten as (2 × 72)7. Use the
Power-Multiply rule to combine the exponents and simplify to 27 ×
714. Quantity A can be rewritten as
. Use the Divide-
Subtract rule to combine the exponents with base 7 to find that
. Therefore, the quantities are equal. The correct
answer is (C).
2. A
Translate and solve each expression. The expression “5 is r percent
of 25” becomes 5 =
× 25. So, r = 20. The expression “s is 25
percent of 60” becomes s =
× 60. So, s = 15, and Quantity A is
greater.
3. A
Plug In for this question. Let h = 3, which makes g = 6. Quantity A
equals
= 6 and Quantity B equals
. Quantity A can be greater
than Quantity B, so eliminate answer choices (B) and (C). Because
g and h are positive integers, Quantity A will always be greater
than 1 and Quantity B will always be less than or equal to 1.
Quantity A will always be greater than Quantity B.
4. B
The average is the sum divided by the number of elements.
Because three elements make up both averages, you can simply
compare the sum of each set. 67 + 78 + 101 + x = 246 + x, and 66 +
79 + 102 + x = 247 + x. Thus, Quantity B is greater.
5. A
Plug In! Say there were 10 million tons in 1988. The percent
increase was
. Then in 1989 there were 10.79 tons, so the
percent increase from 1989 to 1990 was
. Quantity A
must be greater.
6. D
Plug In. Make m = 2 and n = 3. For Quantity A, the weight of 2
peanuts at 3 + 3 mg each is 2 × 6 = 12 mg. For Quantity B, the
weight of 3 almonds at 2 + 3 mg each is 3 × 5 = 15 mg. Eliminate
(A) and (C). Plug In again to see if you can get a different result.
Keep m = 2, and change n to 2. For Quantity A, the weight of two
peanuts at 2 + 3 mg each is 2 × 5 = 10 mg. For Quantity B, the
weight of two almonds at 2 + 3 mg each is 2 × 5 = 10 mg.
Eliminate (B), and choose (D).
7. C
Remember, when you have large exponents, try to break them
down into their prime factors. You can rewrite Quantity A as 527(5)
(115), or 528(115). The quantities are equal.
8. B
For Quantity A, there are three ways to get an even number (these
are 2, 4, 6). So, the probability of “rolling an even” and then
“rolling an even” is
. For multiple independent events,
multiply the probabilities. For Quantity B, there are four ways to
not get a multiple of 3 (these are 1, 2, 4, 5). The probability of “not
rolling a multiple of 3” then “not rolling a multiple of 3” is
. Quantity B is greater than Quantity A.
9. B
There are variables in the answer choices, so Plug In. If r = 2, then
4((2) – s) = −2. Divide both sides by 4 to find 2 – s = −0.5. So, s =
2.5. The target answer is r, which is 2. Go to the answer choices
and plug in 2.5 for s. Choice (B) is the only answer choice that
matches your target of 2.
10. 10.5
Plug In! Let’s say there are 100 employees. 25 percent of the
employees take the subway to work, so
× 100 = 25. Of the 25
employees who ride the subway, 42 percent of them transfer during
the commute, so
× 25 = 10.5. Therefore, 10.5 out of 100
employees transfer lines. This is 10.5 percent.
11. D
Plug In. If a = 3, b = 6, c = 3, d = 5, and e = 10, the value of the
equation is
= 10. Half of 10 is your target of 5. Try
doubling each variable to find the one that yields 5. The only one
that works is doubling d to 10 so that the equation is
= 5.
12. C
For this question, you can FOIL: ( )2 − )( ) − (
)2. This simplifies to 5 − 2
+ 3, or 8 − 2
.
)(
)+(
13. A, C, D, and E
Plug the information given into the formula for the area of a
triangle to learn more about the relationship between x and y: A =
=108. The product of x and y is 216, so x needs to be a
factor of 216. The only number in the answer choices that is not a
factor of 216 is 5. The remaining choices are possible values of x.
14. B
Europe’s electricity production (2,000 megawatt-hours) most
closely matches that of Asia (1,900 megawatt-hours).
15. E
The ratio for North America is 2300 to 0.083 or,
= 27,710.
This is the greatest ratio of any of the continents.
16. A
Africa’s population is 10.6 percent on the pie chart; South
America’s is 7.9 percent. Right away, you can eliminate all of the
answer choices that are smaller than 368. Now you are left with
(A) and (B). Because the question gives you South America’s
population (368 million), you can use a proportion to find the
population of Africa. The proportion would look like this:
, where x is equal to the population of Africa. Crossmultiplying gives you 0.079x = 0.106 × 368, so x = 493.7.
17. A
If the average of 5 crates is 250, then their total = 5 × 250 = 1,250.
To find the high end of the range for the fifth crate, make the other
crates as light as possible: Make the two lightest crates 200 each,
for a total of 400, and the two heaviest crates 300 each, for a total
of 600; together, those four crates weigh 1,000 pounds, leaving 250
pounds for x. Because only (A) sets 250 pounds as the high end,
you can eliminate (B), (C), (D), and (E).
18. B
Substitute 6 for x in the equation, sx = 2sx − 1 + sx − 2 and work
carefully from there. s6 = 2s6 − 1 + s6 − 2, which simplifies to s6 =
2s5 + s4. However you don’t know s5 or s4. Use the equation to find
these missing terms. s4 = 2s3 + s2. and the problem tells you s2 and
s3 are equal to 2. s4 = (2 × 2) + 2, which is 6. Now you need to find
s5. Using the equation, you get s5 = (2 × 6) + 2, which is 14. Now
that you know s5 and s4, go back to your original equation, s6 = 2s5
+ s4, and s6 = (2 × 14) + 6, which is 34.
19. 7
Always draw a figure when one is not provided. In this case, line
segment XZ has a length of 68. Point Y is the midpoint of the
segment, because 2XY = XZ. To find the lengths of these segments,
divide 68 by 2. Segment YZ = 34. Because YZ = 4a + 6, you know
that 34 = 4a + 6, so a = 7.
20. C
Make a spot for each day and fill in the number of guests who
could occupy that spot. Burke has 5 choices for Monday, 3 choices
for Tuesday, 4 choices for Wednesday (because one politician was
chosen on Monday), 6 choices for Thursday, and 10 choices for
Friday (because 4 of the 14 potential guests have already been
chosen). Multiply these to arrive at 3,600 different schedules.
Section 5
1. systematic
The clue is “simple, unambiguous, and unchanging.” The transition
phrase is in other words. The transition maintains the direction of
the clue. Therefore, find a word that means regimented. Systematic
is the best match.
2. obdurate and capitulate
Try working with the second blank first. The second blank is
talking about what a player will be forced to do if he’s stubborn.
The clue is that the “mistakes” the player makes will lead to the
“prevailing strategy of his or her opponent.” Because of these
clues, we know that a word that means “to give in” would be a
good match. Capitulate is the only word that works, as dissent
means to disagree and repudiate means to reject. Now look at the
first blank. The first blank is referring to something all great chess
players know. The clue tells us that they know stubbornness will
almost surely lead to mistakes that force a player to capitulate to
the prevailing strategy of his or her opponent. As you can see, we
needed to solve for the second blank first, as we would not have
known what stubbornness would lead to without doing so. Recycle
the word stubbornness as your word for the blank. Obdurate is the
only word that works for the first blank. Finicky means to be overly
particular, and vituperative means to be combative.
3. corruptibility, venal, and redundancy
The first two blanks are related, but there isn’t a strong clue for
either one in the first part, so let’s start with the third blank. Since
the motif is tiresome, the third blank must mean something close to
“repetitive.” Redundancy matches this. At the end of the paragraph,
each character is bribed…into giving up…beliefs. So the first two
blanks must mean “bribable.” Corruptibility in the first blank and
venal in the second both match this.
4. illegal and unabashedly
For the first blank, the clues “pirating software” and “downloading
software from unapproved sources” describe unauthorized
activities, so illegal is the best fit. Uncommon and difficult are
incorrect because the sentence says that “many people continue to
do so.” If people are doing something despite its illegality and
“almost as if they were unaware that such acts amount to theft,”
you could describe them as acting brashly. Unabashedly is the best
fit.
5. insolvent
The phrase “squandered his life’s savings on unprofitable business
ventures” tells you that the entrepreneur had no money left. The
blank needs a word that means broke. Former and unlikely are
tempting choices, but they don’t match broke. Eliminate them.
Eccentric also doesn’t match, while perturbed only describes the
entrepreneur’s possible feelings. Insolvent agrees with the clue, so
keep it.
6. eschew obfuscation, recondite, and a limpid
The key clue is that the teachers urge students to “use clear, simple
language.” The transition instead indicates that the phrase that goes
into the blank will present an alternative to using clear, simple
language, while the and indicates that the phrase will nevertheless
agree with the clue. Something like “avoid difficult language”
would be best: Difficult language is the alternative to clear, simple
language, but the two phrases still agree because the difficult
language is something to avoid. Thus, eschew obfuscation is best:
Eschew means avoid, while obfuscation means the act of hiding the
meaning of something. Exscind obloquy means to cut out critical
language, while evince ossification means to show excessive
rigidity, neither of which is appropriate here. The second blank
needs a word that means difficult or obscure because teachers call
into question the use of difficult vocabulary; recondite means
obscure and hard to understand. Recreant means cowardly;
redolent means fragrant. The final blank requires a word like clear
because that is the type of language that “conveys one’s meaning
so much more effectively.” Limpid means easily understood, so it is
correct.
7. A and C
Choice (A) is supported because the passage says that myelin
protects the brain’s circuitry. Choice (C) is supported by the fact
that “as humans mature” increasing levels of myelin need to be
produced. While the passage suggests that a lack of myelin leaves
the brain vulnerable, that doesn’t mean that increasing the levels of
myelin will reverse damage.
8. B
In the passage, byzantine refers to the “circuitry inside our nervous
systems.” Previously, the circuitry is described as growing more
complex, so you need to find a word with a similar meaning.
Choice (A) is an alternate meaning for byzantine, but it is not
supported by the passage. Choices (C), (D), and (E) do not have
meanings similar to complex.
9. D
The argument concludes that large universities should utilize workstudy students rather than administrative assistants. The premise is
that a similar strategy realizes a cost savings at small colleges. This
is an argument by analogy. Hence, the argument assumes that there
are similar conditions at small colleges and at large universities.
Choice (D) says that students at universities are just as qualified to
take over the administrative roles as they are in small colleges. In
other words, the administrative jobs at universities are not
appreciably different than those at colleges. For (A), whether the
practice would be of greater benefit to the small colleges is out of
scope. For (B), whether large universities usually depend on small
colleges for ideas is out of scope. For (C), the issue of non-workstudy students is out of scope. For (E), whether anyone has an
easier ride than anyone else is out of scope.
10. A
The first paragraph acts as an introduction to the rest of the
passage. The author notes that in the nineteenth century
“investments became increasingly speculative.” In the last
paragraph, the author explains that due to fluctuating interest rates,
the consol was popular with speculative investors. There is no
support in the passage for (B), (C), or (D). Although the first
paragraph provides a historical framework, as suggested in (E), it
does not provide a way “by which the nature of the nineteenthcentury investor” could be understood.
11. To address the problem, the British government instituted a sinking
fund, using tax revenue to buy back the bonds in the open market.
The second paragraph has five sentences, so this question has five
answer choices. The third sentence begins, “To address the
problem….” This is a clear indication that the sentence describes a
solution to a problem. The correct answer is the third sentence.
12. rarefied and meager
What sort of atmosphere would make Mars the only planet “whose
surface details can be discerned from Earth?” You need a word that
means transparent or thin for the blank. Viscous takes you in the
wrong direction, so toss it. The next choice, ossified, makes no
sense; toss that one too. In contrast, rarefied works well, so hang
onto it. Meanwhile, a copious atmosphere would definitely not be
easy to see through, so cross out that choice. Meager fits nicely and
agrees with rarefied, making those two the correct answers.
13. adversity and tribulation
The clue is “Using the hardships of the Joad family as a model.”
Recycle hardships and use POE. Does reticence mean hardships?
No; cross it out. Adversity works, so leave it. Do the same for the
remaining choices. Only tribulation agrees with hardships, so
that’s the other correct answer.
14. a venerable and an august
The blank is a description of the pyramid. The clue is “imposing
structure” because this is the only other description of the pyramid.
Venerable are the only words that match imposing.
15. noisome and mephitic
The word that fills the blank must describe “the stench of the
livestock,” which is so malodorous that it drives the newcomers
back to the city; it must mean something like, well, “stinky.” Both
noisome and mephitic are appropriate choices. The other words
don’t work; if you were tempted by olfactory, realize that it simply
means “related to the sense of smell” and does not actually
describe a particular scent.
16. B
Choice (B) correctly sums up the purpose of the passage: It
explores the significance—the creation of a military aristocracy
and chivalric culture—of a technological innovation—the stirrup.
Choice (A) is incorrect because nothing in the passage suggests
that this discussion has a basis in recent discovery. Choice (C) is
too broad for the limited subject matter discussed. Choice (D) is
too extreme. Choice (E) is incorrect because the physics, while
important in connecting the stirrup to its social effects, isn’t really
the point of the passage—and, in any event, the physics relates to
cavalry, not artillery.
17. E
Choice (E) is supported by the passage because the sixth sentence
suggests that the development of the barbed lance serves as an
“unusually clear” marker. Choice (A) is incorrect because no
additional subjects for research are brought up in the passage.
Choices (B) and (C) require comparisons beyond the scope of the
information in the passage: No other technology, ancient or
medieval, was discussed. Choice (D), finally, is an extreme
overstatement: Although the stirrup increased the military value of
the horse, nowhere is it suggested that it had previously been
considered militarily insignificant.
18. Stirrups unify lance, rider, and horse into a force capable of
unprecedented violence.
In this sentence, the author says that stirrups improve the ability of
a lance and rider. This is an improvement on the issues discussed
earlier when the author states that a “lance couched under the
rider’s arm, unifying the force of rider and weapon, would throw
its wielder backwards off the horse at impact.”
19. D
Choice (D) describes the organization of the passage. Choice (A)
can be eliminated because the traditional definition is never
amended. Choice (B) can be eliminated because the authorities do
not support the traditional theory. Choice (C) can be eliminated
because no new definition is proposed. Choice (E) can be
eliminated because the “implications of the experiment” are not
rejected.
20. A and B
The author’s dismissal of the traditional definition of randomness
rests upon the premises that the results of the same probabilistic
mechanism will all have the same likelihood of occurring, and, as
such, should be considered equally probable. The passage never
mentions how the results of different probabilistic mechanisms
relate to each other, so eliminate (C).
Section 6
1. A
Solve for x in the top equation,
+2=
, by reducing the right
side: + 2 = 3. Subtract 2 from both sides, and multiply both sides
by 6 to find that x = 6. Solve for y in the second equation, + 2 =
, by reducing the right side:
+ 2 = 3. Subtract 2 from both sides,
and multiply both sides by 3 to find that y = 3. If x = 6 and y = 3,
Quantity A becomes , and Quantity B becomes
= .
2. A
Use the equation distance = rate × time. Bob’s time is 3 hours, and
his rate is 44 miles per hour, so his distance is 3 × 44 = 132 miles.
Inez’s time is 2.5 hours, and her rate is 50 miles per hour, so her
distance is 2.5 × 50 = 125 miles.
3. A
Plug In! Let’s say that the height is 10, the depth is 20, and the
width is 20. If the height is increased by 20%, the new height is 12.
If the depth is decreased by 20%, the new depth is 16 and the width
remains 20. The new volume is 12 × 16 × 20 = 3,840. If you use
those same numbers but make the changes by 40%, the new
volume is 14 × 12 × 20 = 3,360. Quantity A is greater. However,
make sure you switch the numbers to check all possibilities. Make
the height 20, the depth 10 and the width 20. The volume of the
new 3D figure if p is 20 is 24 × 8 × 20 = 3,840. The volume of the
new 3D figure if p is 40 is 28 × 6 × 20 = 3,360. The quantities are
the same regardless of what numbers you plug in. The answer is
(A).
4. D
Draw the figure. Triangle ABC has two adjacent sides, AB and AC,
that are equal in length. The angles that are opposite these sides,
angles B and C, are also equal. One common triangle that has two
equal sides is the 45 : 45 : 90 triangle. If angles B and C were both
45 degrees, then their sum would be 90 and the answer would be
(C). However, we know nothing about the third side of the triangle
so it is possible that this is equal as well, which creates an
equilateral triangle with angles of 60. The sum of the angles in
Quantity A is now 120. You cannot determine which is greater, so
the answer is (D).
5. A
Translate:
= 80, so
k =80, and k = 640. Use this information
in the other equation: k = 640 =
× 80, and solve for y: y =
×
640 = 800. Quantity A is greater than Quantity B.
6. D
Plug in values for each set. If P = {1, 2, 3, 4, 5, 6, 7} and Q = {1, 2,
3, 4, 5, 6}, the range of Q is smaller. Eliminate (B) and (C). If you
change P to {1, 2, 3, 4, 5, 7, 6}, and Q to {1, 2, 3, 4, 5, 7}, the
range of Q is equal to that of P. Eliminate (A), and select (D).
7. A
One way to attack this problem is to list F1 to F11: 10, 13, 16, 19,
22, 25, 28, 31, 34, 37, 40. Notice that F6 through F10 are included
in both quantities, so focus on what’s different. Quantity A is F4 +
F5 and Quantity B is F11. Quantity A is 19 + 22 = 41, and Quantity
B is 40. Alternatively, you know that F4 has had 3 changes from
F1. So, F4 = F1 + 3(3) = 10 + 9 = 19. F5 has had 4 changes from
F1, so F5 = F1 + 3(4) = 10 + 12 = 22. F11 has had 10 changes from
F1, so F11 = F1 + 3(10) = 10 + 30 = 40.
8. C
Plug in a number for n. Let n = 5. Because 5 6 = 30, the product is
30. Add 24 to get 54. Divide by 3 to get 18 as your target. If you
plug in 5 for n in each answer choice, only (C) matches the target:
2n + 8 = 2(5) + 8 = 18.
9. 10
If the average of a and b is 10, then a + b = 20. Likewise, if the
average of c and d is 7, then c + d = 14. If the average of a, b, and c
is 8, then a + b + c = 24. Because a + b = 20, c = 4. If c = 4, then d
= 10.
10. C
To find the area of a square, you need the length of a side. To find a
side, find the distance between two vertices. If A is at (3, 7) and B
is at (3, 12), then the length of a side is equivalent to the difference
in the y-coordinates: 12 − 7 = 5. So, side AB has a length of 5.
Square this to find the area: 52 = 25. The fact that there are
variables for the y-value of points C and D is irrelevant to solving
this problem.
11. B
Get Dylan’s median by putting his weekly sales into increasing
order and finding the middle value. Dylan’s set is {2, 3, 9, 10}, and
his median is the average of 3 and 9, or 6. Next, do the same thing
for Peter’s sales numbers. Peter’s set is {4, 4, 6, 10}, so his median
is the average of 4 and 6, which is 5. The difference between the
medians is 6 − 5 = 1.
12. A
Order doesn’t matter, so remember you must divide by the factorial
of the number of decisions made. For the first topping, you have 6
options. For the second topping, you have 5 options. For the third
topping, you have 4 options.
= 20, (A).
13. E
Because you know the perimeter of the rectangle, you can figure
out that both BC and AD = 5. Thus, the area of the rectangle is 3 ×
5 = 15. The area of the triangle is therefore also 15. Because the
area of a triangle = bh, you can put in the values you know to find
15 = (b × 5) and solve for the base, which is 6. LM is the base of
the triangle, so LM = 6.
14. C
From 1981 through 1984, the ratings for Program y were higher
than they were in the previous year.
15. E
There were 95 million times 80 percent, or 76 million, television
households in 1983. Thirteen percent of them viewed Program y.
76 million times 13 percent (0.13) is 9.88 million, or approximately
10.
16. 500,000
The number of television households that were viewers of Program
x is 3.1 million. The number of television house-holds that were
viewers of Program y is 2.6 million. The difference between the
numbers is 3.1 − 2.6 = 0.5 million, or 500,000.
17. A
Plug In the Answers, starting with (C). If Susan owns 146, Gavin
owns 246, and together they own 392. Matt and Angela together
would own 784, and the total number of houses would be 1,176.
Choice (C) is too large, so also cross off (D) and (E). Try a smaller
number. For (A), if Susan owns 46, Gavin owns 146, and together
they own 192. Matt and Angela together would own 384, and the
total number of houses would be 576.
18.
Plugging In is a great way to tackle this question. Multiply the
denominators of
, , and
together to get 60, which will be an
easy number with which to work. Make the total number of cars
60. 60 ×
= 15 sports cars, and 60 − 15 = 45 sedans. The number
of red cars is 60 ×
= 12. The number of red sports cars is 15 ×
= 5, which means that there are 12 − 5 = 7 red sedans. The fraction
of the sedans that are red is
19. A and B
.
Plug In the Answers. Start with one of the middle values, such as
choice (C). If there are 18 grape candies, then there are 40 total
candies in the jar. The probability of selecting an orange candy is
, or 20 percent. The question states that the probability of
selecting an orange candy is greater than 20 percent, so (C) cannot
work. Values larger than 18 also do not work because when the
denominator becomes larger than 40, the probability becomes less
than 20 percent. The only choices that could work are (A) and (B).
20. E
Plug in for k, and let k = 3. CE is a radius and also half of the
square’s diagonal. If k is 3, then CE is 3, and the diagonal is 6. The
diagonal of a square is also the hypotenuse of a 45 : 45 : 90
triangle. To get the hypotenuse from a side, you multiply by; so, to
get a side from the hypotenuse, divide by
. The sides of the
square are each
. To find the area, square the side to find
= 18. Plug k = 3 into the answers to find one
that yields your target of 18. Choice (E) yields the target of 18.
Appendix: Accommodated Testing
If you plan to request accommodations, you need a copy of the Testing
Accommodations Request Form, which is part of the Bulletin Supplement for
Test Takers with Disabilities or Health-Related Needs. The Bulletin
Supplement
is
at
https://www.ets.org/s/disabilities/pdf/
bulletin_supplement_test_takers_with_disabilities_health_needs.pdf, or
you can request it by phone at 866-387-8602 (toll-free for test takers in the
United States, American Samoa, Guam, Puerto Rico, U.S. Virgin Islands and
Canada) or 609-771-7780. You can also write to:
ETS Disability Services
P.O. Box 6054
Princeton, NJ
08541-6054
Available accommodations include the following:
•
extended testing time (There are no untimed tests.)
•
additional rest breaks
•
test reader
•
scribe
•
sign language interpreter for spoken directions only
•
screen magnification
•
large print
•
trackball
•
audio recording
•
braille
This is not an exhaustive list. ETS will consider any accommodation
requested for a disability or medical condition.
Processing a request for accommodations takes time, so you should submit
your request as early as possible (at least six weeks before you intend to take
the test). The request must include the following:
•
a completed Computer-Based Test (CBT) Authorization Voucher
Request form and the proper test fee
•
a completed Testing Accommodations Request Form
•
a Certification of Eligibility: Accommodations History (COE),
which verifies your use of accommodations at your college,
university, or place of employment. In some cases, the COE is
sufficient to document a disability and can be used in place of
sending full documentation to ETS. If you are eligible to use the
COE in this way, the documentation on file with the college,
university, or employer must meet all ETS documentation criteria.
Please see the Bulletin Supplement for details.
•
documentation (unless you are using the COE as described above)
If you have a psychiatric disability, physical disability or
health-related need, traumatic brain injury, or autism
spectrum disorder, you must submit documentation.
Documentation must also be submitted if your disability has
been diagnosed within the last twelve months, regardless of
the accommodations you are requesting.
The documentation you submit must meet the following criteria:
•
Clearly state the diagnosed disability
•
Describe the functional limitations resulting from the disability
•
Be current: within the last five years for a learning disability or
autism spectrum disorder, last six months for a psychiatric or
physical disability or a health-related need, or last three years for
other disabilities. Documentation of physical or sensory
disabilities of a permanent or unchanging nature may be older if it
provides all of the pertinent information.
•
Include complete educational, developmental, and medical history
relevant to the disability
•
Include a list of all test instruments used in the evaluation report
and all subtest, composite, and/or index scores used to document
the stated disability
•
Describe the specific accommodations requested
•
State why the disability qualifies you for the requested
accommodations
•
Be typed or printed on official letterhead and be signed and dated
by an evaluator qualified to make the diagnosis. The report should
include information about the evaluator’s license or certification
and area of specialization.
If you have a learning disability, ADHD, a physical disability, a psychiatric
disability, a hearing loss or visual impairment, a traumatic brain injury, or an
autism spectrum disorder, refer to the ETS website at www.ets.org/disability
for specific documentation.
ETS will send you an approval letter confirming the accommodations that
have been approved for you.
•
National Paper-Based Testing (PBT)
When you receive your approval letter, you are registered. The
approval letter will identify the testing location and test
administrator. If the testing center cannot accommodate your
request on the scheduled testing date, you will be contacted by the
test administrator to arrange an alternate test date.
•
Computer-Administered Testing (CBT)
The approval letter will include instructions that you must follow
to schedule your test. Do not schedule a CBT test until you
receive your approval letter. When scheduling your test, be
prepared to provide the authorization/voucher number and the
information contained in the letter.
•
Alternate-Format Testing
A representative from ETS Disability Services will contact you to
confirm the accommodations approved for you and to schedule
your test.
BONUS MATERIALS
Admissions and Program Advice
While Cracking the GRE will prepare you for your exam,
the GRE Insider will help you navigate what comes next.
The bonus materials included here contain invaluable
information about degree options, application
considerations, and assorted fields of study. We wish you
the best of luck on your studies and preparation for
graduate school.
Table of Contents
Part 1: Beyond the GRE: Graduate School and More
Part 2: Introduction to Graduate School
Part 3: Graduate School Programs By Type
Art, Design, and Architecture
Biology and Life Sciences
Communications, Journalism, and Media Studies
Computers and Technology
Education and Teaching
Engineering
Environmental Science, Natural Resource Management,
Conservation, and Sustainability
Health Care and Public Health
Humanities and Cultures
Mathematics and Statistics
Physical and Earth Sciences
Psychology
Public Affairs and Policy
Social Sciences
Social Work
Part 1
Beyond the GRE: Graduate School
and More
Graduate schools continue to draw more applicants, more enrollees, and more
graduates in almost every field, with a few exceptions. The most important
thing for a prospective graduate student to know is that there really is no
simple, cookie-cutter way to describe graduate school. While many elements
from program to program are similar, like taking classes, writing papers,
conducting lab or field work, studying advanced theory and sitting for exams,
the category is so broad that until now, we have not found a graduate school
guide that does it justice. The goal of this GRE Insider is to pull back the
covers on specific graduate program areas, examine the data and trends in
each area (as well as associated careers), and highlight opportunities or things
to think about before making this critical life choice.
So Much More Online
To learn more about
graduate school
admissions, check out your
Premium Portal for articles,
advice, and lots more.
One of the best ways we’ve found to describe graduate school is as a critical
stage of career development. In fact for many careers discussed in this guide,
an advanced degree is a requirement in order to get a job in that field. While
some might joke that getting an advanced degree is a great way to put off
getting a “real job”, the reality is that graduate school programs are designed
by professionals and researchers in each field to prepare students for the dayto-day demands and challenges of that specific profession.
For example, there are many master’s programs considered to be
“professional” because they are designed not to prepare graduates for further
study necessarily, but to step right into a recognized profession. These jobs
typically require some kind of certification or licensure that is regulated by
state law, as is commonly the case for counselors, engineers, librarians, social
workers, teachers, and therapists. In such cases, master’s programs are often
geared toward and will include elements that specifically prepare students for
state-regulated exams.
Other master’s programs are also considered professional, not because they
launch students into careers in regulated professions, but because they prepare
students for jobs that require a high level of proficiency in a field that has a
fairly well-defined range of accepted practices. Examples of these fields
include business management, government, information management,
journalism, and museum curation. There are still other master’s programs
designed to prepare students for either further study in the same field or for
careers in which their general skills (though perhaps not their full range of
content knowledge) are applicable. Examples of these programs can be found
in the liberal arts disciplines, such as humanities and social sciences.
Doctoral programs prepare individuals to become experts in a particular field
but also prepare graduates for specific career paths. Most PhD programs, for
example, are designed explicitly to prepare students for careers as professors
in higher education institutions or as researchers in the private, public, or
nonprofit sectors. Other doctoral programs, such as those granting a Doctor of
Psychology and Doctor of Education, are designed to produce practitioners in
selected professions, such as counseling or education. Given that the typical
length of a doctoral program is in the range of five to eight years (depending
on the discipline), it’s even more important for prospective doctoral students
to understand what kind of career they’re preparing for than it is for
prospective master’s students.
Whatever your reasons for reading this guide, we hope it gives you a better
sense of which path to take for success in your future career. Good luck!
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how to guidelines,
and much more!
Part 2
Introduction to Graduate School
The decision to apply to graduate school is one that requires careful thought
about your career goals, awareness of the different paths to reach your goals,
and an understanding of the job market and prospects. In other words, will
your degree help you reach your goals, and ultimately pay off?
For many careers in the graduate arts and sciences disciplines, obtaining a
master’s degree or a PhD is required to be considered for certain jobs. An
advanced degree can also provide an edge in increasingly competitive
industries or for the best jobs in fast-growing industries.
SELECTING A PROGRAM
Programs come in many shapes and sizes. Rather than blitzing every program
with an application, it is best to do your research, focus your attention and
apply to carefully chosen schools. In some fields, it may be important to
consider the prestige of the institution or even the professor with whom you
want to conduct your research. Other fields that require state-based licensure
might cause you to consider the location of your program for the best possible
preparation.
Expert Advice
Visit PrincetonReview.com/
GRE for tried-and-true
GRE and graduate school
advice and information.
It might be helpful to divide potential graduate schools into categories based
on your chances of admission, just as you did when applying to undergrad.
Select two schools you’re fairly certain will accept you, two with whom you
have a fighting chance and one school that you’ll get into if lightning strikes.
This is your target list; add more schools only if you have the time and money
to do so.
Be sure to include making personal connections as part of your research
process. While you can gather a lot of good information about programs
online, make every effort to pick up the phone or go visit a school on your
list. If you are going to spend three to six years in your program, it’s
important to make connections beforehand with the professors, ask questions
and find out how your work (and goals) will be supported. Likewise, talk to
graduate students in the program for a better picture of the atmosphere. It may
be the only way to find out about the things you can’t learn about online.
DEGREE OPTIONS
Do you need a master’s or a PhD? Generally speaking, if you want to conduct
research and development or teach in a postsecondary setting, a PhD is
required.
PhD Degree
PhD programs are designed to give you extensive expertise in a specialized
field, training you to pursue a life in academia as a professor or researcher
(although not all candidates follow this path). Typically you spend five to six
years earning your degree with the first three years focused on required
coursework, writing a dissertation proposal, and developing relationships with
your professors. In years four through six, you take fewer (or no) courses and
focus on writing your dissertation, which is supposed to constitute a new and
meaningful contribution to knowledge in your field.
Some fields offer alternative terminal degrees to the PhD. For example,
engineering offers a Doctor of Engineering Science (EngScD) while a Doctor
of Psychology (PsyD) is a practitioner-based degree with less focus on
research.
Master’s Degree
Just like in college, first-year master’s students take courses to fulfill degree
requirements. However, the workload is heavier, the course topics are more
specific, and much more is expected of you than in college.
At the beginning of the master’s program, you’ll choose (or be assigned) a
faculty member who will serve as your advisor. This person will help you
develop an academic focus and potential topics for your thesis or final project.
As a second year master’s student, you decide on your research focus and—in
one semester or two—complete your master’s thesis or final project. If you
show promise, you may be encouraged to continue toward a PhD.
Fields seeing more job applicants than job opportunities can experience
growth in those opting for a PhD instead of a master’s degree. Be sure to
consider whether the programs you choose offer master’s only or also have
PhD options. Remember that within some programs, you can enroll for a
master’s degree and later choose to pursue a PhD if you are so inclined;
conversely, you can enroll in a PhD program and leave after earning your
master’s if the academic lifestyle fails to entice you further.
LETTERS OF RECOMMENDATION
The value that an objective third-party can provide gives the application
reviewing committee great insight into your value as a candidate for their
program beyond the test scores, GPA, and your own personal statement. Most
programs require three letters of recommendation, so consider that when
selecting a recommender, much weight will be given to recommendations
from academics in your field. However, practice-oriented programs,
particularly ones that value fieldwork as part of your application, would likely
value recommendations from the professionals you worked with during your
internship, job, or fieldwork. If in doubt about recommendations, consider
what kinds of input your audience, in this case the admissions committee,
would most like to help them make their decision, and don’t be afraid to ask
them either.
GRE for Business School?
More and more Business
Schools are accepting
GRE scores for admissions
consideration. Check
out The Best 294
Business Schools
from The Princeton
Review to learn more.
ESSAYS
Putting yourself in the shoes of the admissions committee is a good rule of
thumb for essays while research is the best way of preparing to actually write.
Of course it’s important to talk about the research you would like to pursue in
a graduate program, but make sure you are able to demonstrate a solid
understanding of what the school has to offer. Research their program
strengths as well as their professors’ research and publications; the more your
areas of interest align with the program’s strengths, the easier it will be to
write your essay. Also, be as detail-oriented as possible.
WORK SAMPLES AND INTERVIEWS
Remember that the application and admission process is all about giving the
admissions committee the most complete picture of you and your work as
possible in a relatively short amount of time. Work samples and interviews
are a great way to highlight your strengths as well as make yourself stand out
from other applicants.
Reading through the application requirements early will help you pull
together any necessary requirements, such as a portfolio or audio or video
samples of your work (for areas like performing arts). Some programs will
require or recommend an interview, so don’t be afraid to practice! Talking
about your goals for graduate school with others, and being able to think on
your feet, will give you an edge once you sit down for an interview.
Part 3
Graduate School Programs By Type
ART, DESIGN, AND ARCHITECTURE
Creativity and artistic expression come to mind as the most important skills
for careers in art and architecture. This is especially true in the studio arts or
dramatic and theater arts. So why obtain a graduate degree at all—can’t I just
paint, act, or play music?
Well, yes, but…just as a graduate degree in any other field provides relevant
training and detailed knowledge required for a job in the field, an advanced
degree in the arts gives students an opportunity to develop, refine, and
practice their art with direct access to the resources, materials, and support
they need to grow.
And for art historians, preservationists, conservators, as well as art and film
critics, a balanced background of studying and creating the work provides a
full preparation. Many of these programs focus on history, foreign languages,
and cultural studies.
For the various fields within architecture, there is a unique “marrying” of
creative design and construction with the cultural and social dynamic of the
areas in which architects work, whether it is a streetscape, a renovation of a
historic building, or designing a new home. Programs require that applicants
have a year of college-level math, such as calculus or physics.
Degrees Offered
All areas of art and architecture have experienced growth in advanced degrees
conferred, most notably in architecture and related fields. For many fields in
this area, the terminal degree is a master’s degree, particularly for those
offering the Master of Fine Arts (MFA).
In order to be a licensed architect, one must possess a BArch (a five-year
undergraduate program) or MArch. While a MArch takes about three years to
complete, those entering the program with a BArch can often complete the
program much faster. A Master’s in Interior Architecture (MIA) or Landscape
Architecture (MLA) generally take two to three years to complete, depending
on undergraduate experience, and culminate in a thesis as well as oral and
written exams.
While students in graduate programs for studio and performing arts receive
the terminal degree in their field (MFA), many choose graduate school
because it provides a unique and focused opportunity in which to develop
themselves as artists. Grad school provides the necessary preparation,
resources, and exposure to dramatically influence one’s success as an artist,
writer, performer, or musician. Most programs last two to three years and
culminate in, among other things, a presentation of work produced.
You can find more detailed information to guide you on the right path from
these trade organization websites.
TRADE ORGANIZATIONS YOU SHOULD KNOW
American Film
Institute
The American Film Institute is dedicated to
advancing and preserving the art of the moving
image.
afi.com
American Institute of
Architects
aia.org
News, conferences, education, government affairs
and everything else an architect should know.
American Society of
Landscape Architects
The ASLA provides information on seminars, jobs,
and history of the profession.
asla.org
National Association
of Dramatic and
Speech Arts, Inc.
A professional organization for all dramatics
professionals, including performers, educators,
administrators, and students.
nadsainc.com
National Trust for
Historic Preservation
A not-for-profit organization dedicated to saving
historic buildings, neighborhoods, and landscapes
that form communities.
preservationnation.org
Writers Guild of
America, West
Offers tools for writers of all genres and
professions.
wga.org
Typical Admissions Requirements
Despite the wide range of degrees in art and architecture, all of them
generally require a portfolio as part of the application. Many of the degree
programs in art and architecture are directly linked to creative work, meaning
that a portfolio is the best way for the admissions committee to review the
demonstrated ability of the applicants.
Here are some examples:
•
Acting: live auditions or performance tapes
•
Architecture/Interior Architecture: portfolio of work, typically
created during undergraduate study
•
Graphic Design: portfolio of work
•
Landscape Architecture: portfolio of work that can include
designs, drawings, and photography
•
Playwriting/Screenwriting: at least one full-length dramatic
writing sample
•
Studio Arts: samples, photographs of work
For architecture programs, it is often required to have a bachelor’s degree in
the same or related field while many also require one year of undergraduate
physics and mathematics, such as calculus.
General graduate school requirements:
•
Bachelor’s degree from an accredited college or university
•
Official transcript(s) from all colleges or universities attended
•
GRE General Test scores (different programs require different
minimum scores)
•
TOEFL score (if necessary)
•
Academic letters of recommendation
•
Letter of intent or statement of purpose
•
Application forms
•
Application fee
Some degree programs will also require:
•
Interview or audition
•
Supplemental essays or writing sample
•
Proficiency in a foreign language (art history or architectural
history)
•
Portfolio of work, including audio, video, pictures and samples of
work
BIOLOGY AND LIFE SCIENCES
Biology is a natural science that invloves the study of life and living
organisms. There are many subdivisions of biology, categorized by the scale
and method with which they approach the subject: biochemistry, molecular,
cellular, physiology (organs, tissues, organ systems), and ecology. Within
these subdivisions, one typically focuses on either basic or applied research.
Much of the grant-funded basic research serves as a starting point for applied
research, which finds practical applications of biological knowledge in areas
as diverse as new drugs, treatments, and medical diagnostic tests, increased
crop yields, and new biofuels.
A career path for those who are interested in studying biology and life
sciences is pharmacology. Pharmacologists are often thought of in tandem
with toxicologists, as both research the effects of chemicals on cells.
However, toxicologists examine the effects of poisons on cells while
pharmacologists remain focused on drug-related chemical interactions.
Advanced degrees are required for many jobs in this area. A PhD is required
for researchers seeking funding and post-secondary teachers while a master’s
degree can also be useful in the sales, marketing and publication aspects of
biological sciences.
Degrees Offered in Biology and Life Sciences
An MS in biology and life sciences generally takes two to three years to
complete. Masters programs culminate in a written examination, as well as a
thesis with oral defense. A PhD is generally required for those expecting to
conduct independent research, especially in academia, or for high-level
administrative positions. You can expect to spend five to six years of full-time
study and research in a PhD program.
Some programs, like neuroscience and toxicology, are inherently
interdisciplinary and combine disciplines with other graduate departments.
Those that offer masters degrees in neuroscience are often steps toward PhDs
or combined MD/PhDs. Likewise, a masters degree in toxicology is rarely
seen as terminal—most students spend another four plus years earning their
PhD.
You can find more detailed information to guide you on the right path from
these trade organization websites.
TRADE ORGANIZATIONS YOU SHOULD KNOW
American Board
of Clinical
Pharmacology
Recently created organization that administers an
optional accreditation for clinical pharmacologists.
abcp.net
American
Institute of
A membership organization advancing research,
education, and public policy issues for the biological
Biological
Sciences
sciences. Publishes a peer review journal.
aibs.org
Society for
Neuroscience
sfn.org
Association of
Zoos and
Aquariums
World’s largest organization of scientists and
physicians devoted to understanding the brain and
nervous system. Includes an extensive Higher
Education and Training section.
Links to job opportunities, conferences, and
professional training opportunities.
aza.org
Society for
Human Ecology
The society is an “international interdisciplinary
society” whose mission is to promote “the use of an
ecological perspective in research and application.”
societyforhumanecology.org
Society of
Toxicology
Plenty of information about schools, degrees, grants
and fellowships, links to career information, and other
resources.
toxicology.org
Typical Admissions Requirements
While many programs in biology and biological sciences might not require a
specific major for admission, if they require a GRE Subject Test in either
Biology or Biochemistry, Cell and Molecular Biology, then an undergraduate
major or significant coursework is typically the best preparation.
General graduate school requirements:
•
Bachelor’s degree from an accredited college or university
•
Official transcript(s) from all colleges or universities attended
•
GRE General Test scores (different programs require different
minimum scores)
•
TOEFL score (if necessary)
•
Academic letters of recommendation
•
Letter of intent or statement of purpose
•
Application forms
•
Application fee
•
Interview
Some degree programs will also require:
•
GRE Subject Test: Biology
•
GRE Subject Test: Biochemistry, Cell and Molecular Biology
•
Curriculum vitae
•
Research statement (as part of letter of intent)
COMMUNICATIONS, JOURNALISM, AND
MEDIA STUDIES
Radio, TV, Internet, smartphones and tablets…the evolution of media
consumption has driven dramatic changes and opportunities in the field of
communications, journalism, and media studies.
Companies such as Google, Facebook, YouTube, Tumblr, Vine, and Twitter,
along with easy-to-use technology and publishing tools (digital cameras, free
blogging sites) give anyone with access to a computer or smartphone the
opportunity to reach an audience with their message. Twenty-four-hour news
channels (and their companion websites or social media outlets) mean that
news and information are pumped out at an unprecedented speed and volume.
Just as important in this evolution are the communications professionals who
either create, or react to, the news on behalf of their employers. These days, it
goes beyond for-profit companies and government organizations to include
nonprofits, school districts, and yes, celebrities and personalities.
So what distinguishes an amateur from a professional? An advanced degree in
communications, journalism or media studies provides a graduate student
with the skills she needs to be an effective and educated resource, honing any
raw skills and nurturing a passion for the field. With rapidly changing
technologies and new social media outlets, students can learn the latest trends
and technologies to understand how they can work together for the biggest
impact. A graduate degree can also give professionals in this area of study the
solid background and experience to strike out on their own with more
credibility.
Degrees Offered
The few PhDs pursued in this field are for post-secondary teaching and
research, though there has been a a small surge in PhDs with 31-percent
growth between 2008–2009 and 2013–2014. The majority of the 32,000
enrollees in this discipline pursue a master’s degree.
Though programs vary by institution, if you want to report the news (writing,
broadcasting, or publishing), you’d probably want to look at journalism
programs. If you want to study forms of communication, methods, culture, or
media, then you probably want to look into communications programs. Again,
research both disciplines (sometimes housed in the same department) to
determine the best path for your career.
The Master of Arts tends to be more common than the Master of Science in
journalism, and the differences between programs vary from institution to
institution. Remember, a broad knowledge of history and current events
strengthens the quality of your work in the field while perseverance and
experience tend to play a big role in making a good journalist great. Try to
find programs that teach more than just core skills and feature a depth of
writing experiences and frequent fieldwork. Some programs also provide the
opportunity to focus in a particular subject area such as health care, science,
business, etc. Master’s programs in communications also offer a range of foci
including advertising and marketing, politics, law, public policy, and the
global and cultural aspects of communication in society or within an
organization.
Depending on your career goals and your industry of preference, combined or
interdisciplinary degrees can be found at many institutions, depending on
where they house their communications, journalism and media studies
programs.
MA Journalism (2–3 years)
MS Journalism (1–2 years)
MA Communications or Mass Communications (2–5 years)
BA / MA Journalism (5 years, starting junior year of college)
PhD Communications or Journalism (5–7 years, including dissertation)
You can find more detailed information to guide you on the right path from
these trade organization websites.
TRADE ORGANIZATIONS YOU SHOULD KNOW
The Associated
Press
The AP is the momma bear of all journalistic agencies.
ap.org
The Poynter
Institute
poynter.org
From its “Mission & History” statement: “The Poynter
Institute…is the world’s leading instructor, innovator,
convener and resource for anyone who aspires to engage
and inform citizens in 21st Century democracies.”
American
Society of
Magazine
Editors
The American Society of Magazine Editors is the
professional organization for print and online magazine
editors. Its website lists jobs, hosts discussion boards, and
offers courses for junior editors, among other things.
magazine.org/
asme
National
The National Communication Association advances
Communication communication as the discipline that studies all forms,
Association
modes, media and consequences of communication
through humanistic, social scientific and aesthetic inquiry.
natcom.org
Find resources, publications, and careers on their website.
National Press
Photographers
Association
Promotes photojournalism with competitions, workshops
and seminars, and job listings.
nppa.org
Typical Admissions Requirements
Experience in journalism, whether in the classroom or on the streets, is a plus
but not required. Writing samples from undergraduate study, undergraduate
GPA, recommendations, essays and, in some cases, GRE scores are required.
While undergraduate prerequisites vary, most programs require a bachelor’s
degree in a related field.
General graduate school requirements:
•
Bachelor’s degree from an accredited college or university
•
Official transcript(s) from all colleges or universities attended
•
GRE General Test scores* (different programs require different
minimum scores)
•
TOEFL score (if necessary)
•
Letters of recommendation
•
Letter of intent or statement of purpose
•
Academic or professional writing samples
•
Application forms
•
Application fee
*Not required for all programs
COMPUTERS AND TECHNOLOGY
The field of computers and information technology includes three main
disciplines: computer science, information systems, and information
technology. The fields do overlap in terms of certain training and curriculum.
A bachelor’s degree is sufficient for many careers in these fields, but for those
looking to advance within their organizations, manage teams, or teach, a
graduate degree boosts your potential. In addition to Master of Science
degrees, one might consider an MBA with a focus in technology.
Graduate programs focus on both theoretical frameworks, along with applied
research and lab work. Because this is a rapidly changing field, a strong
theory-based knowledge coupled with a practical orientation keeps students
not only current, but in some cases on the cutting edge of advancing new
technologies.
Computer scientists contribute to new technologies, including interactive
multimedia and virtual reality systems. Time is divided between class and lab
work to ensure that students are equipped with the necessary skills in software
development, systems development, and new computer systems creation.
Information technology covers the entire spectrum of computer-based
content, and those who undertake study in this field will learn about it all.
Courses cover computer hardware and software; how to view and send
information by computer plus how to adapt, control, and improve the
experiences had by computer users. In addition, graduate students will learn
how to create and modify the very systems that transmit the information—and
how to best distribute that information to the target audience. Study will also
include web-based computer applications, the fundamentals of e-commerce,
the importance of web security, ethical issues and finally, how information
technology affects business and society.
Those interested in more of a management-based career might want to
consider a graduate program in management information systems (MIS).
Studies in MIS will include management strategies and theories, how
management can best use information systems and applications and security.
You’ll also learn how skillful use of information systems can lead to business
solutions, help with decision-making and ways to improve the corporation.
Degrees Offered in Computers and Technology
Advanced degrees in computer science include either the Master of Arts or
Master of Science, and of course, the PhD. Graduate students study broad,
theoretical frameworks and then exercise that knowledge through lab work.
Many who choose to pursue a doctorate select a concentration. Be sure to
look for programs that produce and contribute to the latest research in
computer science given that it is a rapidly changing field. Degree programs
related to computer science include:
•
Information Science
•
Information Technology
•
Management Information Systems (MIS)
•
Systems Engineering
•
Web/Multimedia Management
Graduate work in information technology covers everything from hardware
and software to managing and transmitting the information as well as the enduser experience. Your hands-on graduate work culminates in a MS in
information technology or information technology and management. Students
wishing to teach or pursue more research can advance with a PhD program in
either information technology or another computer-related field. For those
interested in a more management-based IT career, consider an MS in
management information systems (MIS), which prepares graduate students
for management careers in technology. Alternatively, one could pursue an
MBA with a focus or concentration in information systems.
You can find more detailed information to guide you on the right path from
these trade organization websites.
TRADE ORGANIZATIONS YOU SHOULD KNOW
Association of
Information
Technology
Professionals
Education, peer support, and information for IT
professionals in government, industry and academia.
aitp.org
HDI
thinkhdi.com
Society for
Information
Management
The largest association for IT service and support
professionals produces numerous publications, hosts
several symposiums and conferences each year, and
certifies hundreds of help desk and service desk
professionals each month.
Provides information and a community of shared
experience among professionals.
simnet.org
TechAmerica
Public sector and public policy department of CompTIA,
the IT industry trade association.
TechAmerica.org
EDUCATION AND TEACHING
Many enter the teaching profession in order to make that connection with
children or young adults where the proverbial light bulb goes on and the
student “gets it.” While the monetary rewards in teaching may not be
substantial, the personal satisfaction in helping students develop intellectually
and socially is a driving force behind the decision to teach.
Thanks to projected population growth, enrollment increases are expected
across all grade-levels and so the outlook for teaching professionals is good.
However, increased demands have been placed on teachers and administrators
alike, meaning that it takes a special talent to be a successful classroom
teacher or an effective administrator. Increased accountability, emphasis on
standardized testing, more ESL students and growing classroom sizes are just
a few of the challenges new teachers face every day. While the number of
advanced degrees has decreased overall, and Master’s degrees have decreased
by 6 percent, the number of doctorates has increased by 21 percent. Demand
for teachers continues to be highest for those who will work in rural or urban
areas, or those who specialize in bilingual education, math and science, or
special education.
Degrees Offered in Education and Teaching
There are literally thousands of programs in education, many of which require
a teaching credential. Those who do not have a valid teaching credential or
even an undergraduate background in education should look for programs that
allow students to pursue licensure during their course of study.
For special ed (MS, MEd), and elementary and secondary school teaching
(MS, MA, MEd), MS and MA programs usually require students to write a
culminating thesis based on classroom research, whereas MEd programs
usually do not. MS programs may also require more class work in
methodology and research than MA or MEd programs. Most of these
programs can be completed in one to two years with flexible part-time,
evening, or summer options for current teachers.
Master’s programs in educational administration usually span about one or
two years and require successful performance in advanced level coursework,
as well as participation in a practicum, research project, or internship. Some
schools also require students to complete a master’s thesis. After completing a
master’s degree in educational administration, students may choose to
continue their studies in an Educational Specialist (EdS) program, designed
for students who want to engage in advanced fieldwork, internship
experience, or research in a specific area of education. Doctoral programs in
educational administration usually focus on research or public policy as it
relates to school leadership.
Post-secondary teachers require a PhD or the terminal degree in the field in
which they want to teach (for example, an MFA to teach arts and music at the
post-secondary level). See also the Humanities and Cultures section for more
information on many post-secondary fields.
More Reading
To learn more about
teacher certification,
check out our book
Cracking the Praxis,
2nd Edition.
You can find more detailed information to guide you on the right path from
these trade organization websites.
TRADE ORGANIZATIONS YOU SHOULD KNOW
AASA: The
School
Superintendents
Association
AASA is a national association of school system leaders.
Their website contains a job board, industry related
articles, membership information, and links to state
associations.
aasa.org
National
Association for
Bilingual
Education
(NABE)
A professional association for bilingual educators. The
site has information about the field and a great page of
links to related sites.
nabe.org
National
Association of
State Boards of
Education
The National Association of State Boards of Education
will help you find information about state-specific school
districts including links about certification requirements,
teaching standards, and a section on early childhood
education.
nasbe.org
National
Science
Teachers
Association
The National Science Teachers Association is a national
organization of science teachers. Check their web site for
information on conferences, news, publications, and other
education resources.
nsta.org
United States
Department of
Education
Information about Every Student Succeeds and other
federal programs on education.
ed.gov
Typical Admissions Requirements
Students applying to education and teaching programs typically have several
years of teaching or administration experience along with a valid teaching
credential. However, some master’s level programs will include a certification
component for students interested in entering the education field without prior
experience or certification.
General graduate school requirements:
•
Bachelor’s degree from an accredited college or university
•
Official transcript(s) from all colleges or universities attended
•
GRE General Test scores (different programs require different
minimum scores)
•
TOEFL score (if necessary)
•
Academic letters of recommendation
•
Letter of intent or statement of purpose
•
Application forms
•
Application fee
Some degree programs will also require:
•
Interview
•
Miller Analogies Test (MAT)
•
Portfolio (Arts Education)
ENGINEERING
Engineering is a long-respected field leading to many challenging and
exciting careers that draw upon creativity, innovative thinking, and a strong
foundation in math and science. Engineers are the link between scientific
discovery and the commercial application and production of those innovations
in society.
There are over 1.4 million engineers employed in the United States, with 4
percent growth expected through 2024. All advanced degrees conferred grew
5 percent through 2013–2014, and PhDs saw an impressive 30 percent
growth. With ancient roots dating back to the building of the pyramids,
modern engineering trends show a dramatic increase in biomedical
engineering as well as higher demand for infrastructure projects to preserve
aging buildings, bridges, and transportation systems. Electrical engineering
programs are the largest, with nearly a third of all engineering student
enrollment.
Degrees Offered
Engineering offers a wide range of degree programs, each of which contains
many concentrations for specialization. For example, a civil engineer could
specialize in construction, hydrosystems, structural, or transportation
engineering.
Most master’s programs are one to two years in length. While not all
programs require a relevant bachelor’s degree, they do require a strong
background in math, science, and engineering undergraduate courses. For
those interested in research or academia, further study is required for a
Doctorate in Engineering. An alternative to the PhD is a Doctor of
Engineering Science (EngScD).
You can find more detailed information to guide you on the right path from
these trade organization websites.
TRADE ORGANIZATIONS YOU SHOULD KNOW
National Society
of Professional
Engineers
nspe.org
The National Society of Professional Engineers has the
scoop on all the latest technologies and licensing
regulations.
American
Engineering
Association
The American Engineering Association provides a
support system for all engineers. Included on the site are
links to information for computer and electrical
engineers.
aea.org
American
Society of Civil
Engineers
The American Society of Civil Engineers is the best
clearing house for the field. This is the place to look for
news, jobs, and licensing information.
asce.org
Institute of
Electrical and
Electronics
Engineers
IEEE is the most complete site dealing specifically with
electrical engineering. It also contains job information,
interesting articles on the field, and even a virtual
museum.
ieee.org
ASME
asme.org
NASA (National
Aeronautics and
Space
Administration)
An excellent resource for both experienced workers and
newcomers to the field. They have a very thorough
Career & Education section.
The site includes recent news about NASA and its
accomplishments.
nasa.gov
Typical Admissions Requirements
Most graduate engineering programs look for substantial coursework in math
and science at the undergraduate level, and some require specific classes or
majors within the field. Be sure to carefully review admissions requirements
well in advance so you can meet all requirements before you apply.
Depending on the program, schools might require a minimum GPA.
General graduate school requirements:
•
Bachelor’s degree from an accredited college or university
•
Official transcript(s) from all colleges or universities attended
•
GRE General Test scores (different programs require different
minimum scores)
•
TOEFL score (if necessary)
•
Letters of recommendation
•
Application forms
•
Application fee
Some degree programs will also require:
•
Interview
•
Letter of intent or statement of purpose
•
Supplementary essays
ENVIRONMENTAL SCIENCE, NATURAL
RESOURCE MANAGEMENT, CONSERVATION,
AND SUSTAINABILITY
As green issues grow in importance, popularity, and sometimes controversy,
the professional fields that employ environmental scientists, conservationists,
and natural resource managers are expanding.
In fact, the National Center for Education Statistics did not even track
graduate enrollment in natural resources and conservation in the mid 1990s,
but reported 22,000 graduate enrollees as of 2011–2012. Job growth in this
sector is projected at 11 percent through 2024.
Whether driven by the science behind these issues or the laws and policies
(informed by the science and social issues) that impact the environment,
people enter this field to make a difference and help keep our planet in good
shape for the next generation. Many schools create interdisciplinary programs
to encompass the various subjects that impact this field; one might take
courses across departments of biology, law, anthropology, sociology, and
business or economics. In addition, graduates students can specialize in their
particular area of interest, whether more focused on wildlife, water, forestry,
land-use, etc.
In general, environmental science takes a more scientific, research-based
approach to the problems while environmental studies encompasses the
social, historical, political, and legal aspects of the field, with a foundation in
scientific data. Be sure to research a specific school’s program description and
curriculum, as environmental studies is open to interpretation by a school’s
faculty and departments. If your interest area is specific to forestry, flora and
fauna (wildlands), fisheries and aquatic life, or mammals (wildlife), there are
master’s and PhD programs for these subject areas. Also, think about your
geography, as your fieldwork can be greatly enhanced by the location of your
graduate program.
Degrees Offered
While there are opportunities for those with bachelor’s degrees to work in this
field, master’s degrees provide opportunities for advancement and
management positions including leading research teams or controlling the
direction of projects. Master’s degree programs also give students an
opportunity to conduct in-depth research employing scientific methods and
fieldwork, and exploring the broad spectrum of environmental issues, like the
laws and policies that impact this discipline. Of course, a PhD is required for
some teaching, research, or senior positions at policy institutes and
government agencies.
When choosing your degree program, consider whether you want a broad
approach to natural sciences with a specific focus area or would prefer a
scientific approach within your area of focus. Degree options include:
•
MA or MS in Environmental Studies/Science
•
PhD in Environmental Studies/Science
•
Master of Forestry, MS or PhD Forestry
•
MS or PhD Natural Resources Management and Policy
•
MS or PhD Wildlife or Wildlands Science and Management
You can find more detailed information to guide you on the right path from
these trade organization websites.
TRADE ORGANIZATIONS YOU SHOULD KNOW
Joint Forestry Team
Different organizations join resources to make
recommendations that result in coordinated
jointforestryteam.org interagency delivery of forestry and conservation
assistance for working forests, farms, and ranches:
USDA-National Resources Conservation Service
(NRCS), the National Association of State Foresters
(NASF), the National Association of Conservation
Districts (NACD), and the USDA Forest Service
(USFS).
National Audubon
Society
For more than a century, the Audubon Society has
been committed to conserving and restoring natural
ecosystems, particularly for birds and wildlife.
audubon.org
Natural Resources
Conservation
Service
Established by Congress in 1935 as the Soil
Conservation Service, this agency’s name was
changed in 1994 to reflect its broadening scope.
nrcs.usda.gov
League of
Conservation Voters
lcv.org
A national non-profit that works to keep
environmental issues as national priorities, often
through grass-roots campaigning, awareness, and
education.
Typical Admissions Requirements
Depending on your area of focus, programs may look for a variety of
coursework, including anthropology, biology, sociology and more.
Undergraduate GPA, recommendations, essays, and GRE scores are required.
While undergraduate prerequisites vary, some programs look for an
undergraduate degree in a field such as the natural sciences, social sciences,
or engineering. For students pursuing subject matter related to policy or
economics, schools will look for relevant majors/coursework in those areas.
General graduate school requirements:
•
Bachelor’s degree from an accredited college or university
•
Official transcript(s) from all colleges or universities attended
•
GRE General Test scores (different programs require different
minimum scores)
•
TOEFL score (if necessary)
•
Letters of recommendation
•
Letter of intent or statement of purpose
•
Application forms
•
Application fee
Some degree programs schools also require:
Specific coursework in a related field. Some schools give conditional
acceptance until students earn credits for a specific area that is lacking.
HEALTH CARE AND PUBLIC HEALTH
The field of health care is experiencing explosive growth due to the growing
elderly population and technological advances in the treatment and diagnosis
of illness, disease, injury, and other physical and mental impairments. With a
fantastic job outlook, all graduate degrees conferred grew 40 percent in five
years (from 2008–2009 to 2013–2014). Many careers in this field require
advanced education and/or specialization, and the number of advanced
degrees conferred mirrors the growth pattern in this industry, with a 55percent increase in master’s degrees and 23-percent increase in PhD’s
conferred (from 2008–09 to 2013–14).
Degrees Offered in Health Care and Public
Health
Graduate degrees in health care or public health are required for many careers
in this field. For audiologists, speech pathologists, occupational or physical
therapists, and many other health careers, a master’s degree or professional
degree prepares you for work with patients whether in hospitals, clinics,
ambulatory care centers, or physicians’ offices. Some nurses and public health
graduates interested in administration or management pursue joint degrees,
such as a joint MBA program.
Growth in the health care industry is evidenced by the dramatic growth seen
in advanced degrees conferred. Particularly notable is the rise in the number
of doctorates or professional degrees, which grew to over 64,000 in 2013.
Further Reading
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Some master’s degree programs are coupled with undergraduate programs
while others allow you to enter without a specific bachelor’s degree as long as
you meet prerequisites. Some examples include Master of Science in Nursing,
Master in Public Health or Master of Science in Public Health, Master of
Science in Physical Therapy, etc. Another possible career path in health care
is the Doctor of Medicine (MD) or the Doctor of Osteopathic Medicine (DO).
Admission to these programs is very competitive and it’s worth noting that
admission requires a strong background in sciences and math as well as solid
MCAT scores.
You can find more detailed information to guide you on the right path from
these trade organization websites.
TRADE ORGANIZATIONS YOU SHOULD KNOW
American
The American Association of Nurse Practitioners is an
Association of
advocacy and policy oriented organization of nurse
Nurse Practitioners practitioners.
aanp.org
American College
of Epidemiology
The American College of Epidemiology is a
professional organization dedicated to continued
education for epidemiologists and their efforts to
acepidemiology.org promote the public health.
American Physical
Therapy
Association
The American Physical Therapy Association has
scholarship listings, seminar information, and related
resources.
apta.org
American Public
Health Association
(APHA)
The APHA is an organization dedicated to promoting
research on issues in public health and influencing
public health policies for over 125 years.
apha.org
Nursing Center
nursingcenter.com
The Nursing Center is a resource for professional
nurses. Its website offers articles, job listings, CE
activities, and message boards.
Typical Admissions Requirements
Requirements vary depending on the program you wish to pursue—be sure to
read about specific prerequisites for the schools on your list. Most professions
in this field need majors or coursework in the sciences and statistics while
business and economics are common admissions requirements for managerial
positions.
Trends in Health Care and Public Health
Technological advances in healthcare mean more options for treating illnesses
and diseases. Coupled with an increased emphasis on preventative care, this
will drive demand for more nurses, already the largest healthcare occupation
at over 2.75 million.
Hospitals are one of the largest employers of healthcare workers; despite this,
hospitals will see a slower rate of new jobs because clinics and other
outpatient care sites are growing in use.
Fourteen of the top twenty fastest growing occupations (across all
occupations) are healthcare related, meaning that the industry as a whole
should see 18-percent growth in jobs through 2024.
The aging baby boom population will increase demand in specialties like
occupational therapy, physical therapy, audiology, and speech pathology.
HUMANITIES AND CULTURES
Socrates taught the adage “Know thyself.” Our need to find meaning and
connect with one another runs deep in our humanity. The various degree areas
of focus in the humanities and cultures provide a context that allows us to
better understand “who we are” through the study of literature, culture, gender
or ethnic identity, philosophy, religion, and even the very languages we speak.
The analytical thinking and writing skills required for many of these
disciplines translate well to many jobs in our modern economy.
Post-secondary teaching and writing opportunities show solid competition for
jobs, but job outlook remains fair depending on the area pursued. Growth in
advanced degrees has remained steady at 9 percent over a five-year period
(from 2007–08 to 2012–13), however there was a 2 percent dip in between
2013 and 2014.
Degrees Offered in Humanities and Cultures
Most master’s degree programs in humanities and cultures take one to two
years to complete, with a culminating thesis and exams. This is true for
creative writing, but students also have the option to pursue a Master of Fine
Arts, which usually takes two to four years and typically requires a
manuscript of publishable quality to complete the program.
Those who choose to go on to pursue a PhD can expect to spend five to seven
years fulfilling course requirements, writing a thesis and ultimately, defending
it orally. Many PhD programs also have written exam requirements. For
degrees in comparative literature and even other areas of literature, there are
also foreign language requirements.
A master’s level (MA or MS) degree in linguistics covers core areas of
language structure, field methods, and research. Programs may be class-based
or thesis-based; most take about two years. A PhD in linguistics may take an
additional three to four years. Most doctoral programs encompass master’s
level material but focus on theoretical topics in language structure, language
acquisition, and processing.
You can find more detailed information to guide you on the right path from
these trade organization websites.
TRADE ORGANIZATIONS YOU SHOULD KNOW
American Academy The world’s largest organization of academics
of Religion
researching and teaching religion-related topics.
aarweb.org
American
Comparative
Literature
Association
Provides links to journals, prizes, conferences, and
also to affiliated associations and research sources.
acla.org
Linguistic Society
of America
This is the largest linguistic society in the world; an
interest in the field is the only requirement for
membership. In addition to a regularly published
linguisticsociety.org journal, Language, the LSA hosts annual meetings
and summer institutes
The Modern
Language
Association of
America
Information on periodicals, conferences, readings,
jobs, and style guides. It also provides a quarterly
newsletter and links to accredited universities.
mla.org
The Voice of the
Shuttle
An online compendium of sites for academic
research. It contains searchable areas from multiple
disciplines in the humanities.
vos.ucsb.edu
Typical Admissions Requirements
Admissions requirements vary across the broad spectrum of programs within
humanities and cultures, but most programs require excellent writing skills, so
essays, statement of purpose, and/or academic writing samples will often be
required as part of the admissions process. For American or English literature
as well as comparative literature, be ready to take the GRE Subject Test in
Literature in English in addition to the GRE.
General graduate school requirements:
•
Bachelor’s degree from an accredited college or university
•
Official transcript(s) from all colleges or universities attended
•
GRE General Test scores (different programs require different
minimum scores)
•
TOEFL score (if necessary)
•
Academic letters of recommendation
•
Letter of intent or statement of purpose, essays
•
Application forms
•
Application fee
Some degree programs will also require:
•
Curriculum vitae
•
GRE Subject Test: Literature in English
•
Academic writing samples
MATHEMATICS AND STATISTICS
Mathematics is a unique field that requires more than just a mastery of
existing techniques and theories; it actually gives mathematicians the
opportunity to discern the need for and test the creation of new theories.
The advanced study of mathematics and statistics develops problem solving
and critical thinking skills that are sought after and applied in many different
career paths. An advanced degree in mathematics or statistics is required for
university-level teaching and advanced research.
When looking for graduate programs, know that academic institutions vary
the way they structure their programs and departments. Some statistics
departments are housed within the mathematics department while others are
separate. Some schools break out applied mathematics to differentiate it from
“pure” mathematics. While not all professionals agree on the exact
distinctions, applied math generally refers to the mathematical methods used
in specific areas such as business, science and engineering, or industries like
insurance, healthcare, and finance. Applied math often results in the
development of new mathematical models, which are in turn studied in pure
mathematics, which covers more theory and generalities.
As a pure mathematician, career opportunities are more competitive unless
the degree is coupled with an area of industry focus. Some careers that benefit
from advanced math and stats knowledge are physics, actuarial science,
biostatistics, engineering, operations research, computer science, marketing,
business and industrial management, economics, finance, chemistry, geology,
life sciences, behavioral sciences, and many other fields.
Degrees Offered in Mathematics and Statistics
Master’s degrees can be pursued on their own, but are also pursued by
doctoral candidates in other related fields such as computer science,
engineering fields, physics, business, finance, etc. Schools often have thesis
and non-thesis options, which in some cases means the MA option is nonthesis and the MS option is thesis track, but this is not always the case. Other
schools track the MA option for secondary school or community college-level
teaching, but again, programs vary. Read the department descriptions about
each option to see how it best fits to your intended career path. Degree
options include:
•
MS or MA Mathematics (12–24 months)
•
MS or MA Applied Mathematics (12–24 months)
•
MS or MA Statistics (12–24 months)
•
PhD Mathematics (4–6 years)
•
PhD Statistics (4–6 years)
The PhD track is best suited for teaching and research at the university level,
or for quantitative research and development in industry or government.
TRADE ORGANIZATIONS YOU SHOULD KNOW
American
A rich resource for news and events, publications, jobs, and
Mathematical research (as you might expect, AMS has lots of data and
statistics on education and careers in mathematics).
Society
(AMS)
ams.org
American
Statistical
Association
The world’s largest community of statisticians provides
resources, news and events, career information, and even
scholarships and grants for statisticians worldwide.
amstat.org
Data.gov
A website run by the federal government; its goal is to make
executive branch data sets accessible and available to the
public. Among other things, it encourages app development,
and community interaction by area, such as energy or
health.
Society for
Industrial
and Applied
Mathematics
SIAM’s mission is to build cooperation between
mathematics and the worlds of science and technology
through publications, research, and community.
siam.org
Typical Admissions Requirements
•
Minimum GPA
•
Major in math, statistics, or related area with a background in
calculus (multivariate, probability) and linear algebra
Some programs require the GRE Subject Test in Mathematics.
Some graduate programs in mathematics (typically pure math PhD track)
have a foreign language requirement, particularly in French, Russian, or
German. Many programs require knowledge of a programming language.
General Graduate School Requirements
•
Bachelor’s degree from an accredited college or university
•
Official transcript(s) from all colleges or universities attended
•
GRE General Test scores* (different programs require different
minimum scores)
•
TOEFL score (if necessary)
•
Letters of recommendation
•
Letter of intent or statement of purpose
•
Writing samples
•
Application forms
•
Application fee
*Not required for all programs
PHYSICAL AND EARTH SCIENCES
A highly analytical and research-intensive area, the physical and earth
sciences attempt to understand the universe and everything in it: the earth’s
atmosphere, the earth itself and its oceans, right on down to subatomic
particles.
To observe, measure, interpret and develop theories, the understanding and
use of mathematics is a critical component to these sciences. Knowledge
gained in research is used to design new technologies. Many of these
scientists opt to apply their skills in engineering.
For most jobs in physical and earth sciences, an advanced degree is required.
Enrollment, as well as the number of degrees conferred, has shown consistent
growth to fill these jobs. Projected job growth is forecasted to average 8
percent in all areas (2014–2024 projection), but closer examination shows
more competition in areas like chemistry (the largest field in the group), and
very good job opportunities in hydrology and geosciences. Funds from the
federal government are helping to boost job growth in the physical sciences as
well. In 2007, Congress passed the America COMPETES Act (reauthorized
by Congress in 2010), which funds government agencies employing physical
scientists to boost the nation’s standing in technology and innovation.
Typical Admissions Requirements
Without an undergraduate degree in the same field, which many programs
will require, a strong background in the physical sciences and mathematics is
preferred, and is the best preparation for graduate school. In addition to the
GRE, schools may require the GRE subject test in Chemistry or Physics.
Given the research-oriented nature of a graduate degree in physical sciences,
be sure to do your homework about the areas of research among the faculty,
so you can tailor your letter of intent or statement of purpose to the research
or specialty you want to pursue in graduate school.
TRADE ORGANIZATIONS YOU SHOULD KNOW
American
Chemical
Society
acs.org
Publishes numerous scientific journals and databases,
convenes major research conferences, and provides
educational, science policy, and career programs in
chemistry. Also grants more than $22 million in funds for
basic research.
American
Institute of
Hydrology
Establishes the standards for the certification of
hydrologists; encompasses both student and professional
chapters.
aihydrology.org
American
Umbrella society for physicists and astronomers, students,
Institute of
Physics
and teachers of those subjects. Publishes journals, and
website lists valuable resources and job postings.
aip.org
American
Provides certification, as well as a wealth of information
Meteorological about the field including job postings and grants.
Society
ametsoc.org
American
Physical
Society
aps.org
Second largest organization of physicists which hosts
meetings, publishes journals, and provides career
information through its website.
General graduate school requirements:
•
Bachelor’s degree from an accredited college or university
•
Official transcript(s) from all colleges or universities attended
•
GRE General Test scores (different programs require different
minimum scores)
•
TOEFL score (if necessary)
•
Academic letters of recommendation
•
Letter of intent or statement of purpose
•
Application forms
•
Application fee
Some degree programs will also require:
•
GRE Subject Test: Chemistry
•
GRE Subject Test: Physics
•
Interview or campus visit
•
Relevant work experience
PSYCHOLOGY
Psychology is a science that attempts to better understand mental processes
and predict human behavior through careful observation, study and research.
It is a popular field with many areas of focus, from industrial and
organizational (that applies the principles of psychology in the workplace) to
clinical or counseling psychology, where one can focus on children, families,
or senior citizens, to name a few.
In general, those interested in psychology follow either a research/teaching
track or a counseling track. Psychologists work in schools, hospitals and
assisted living centers, and teach or conduct research in schools, colleges, and
universities.
About 34 percent of all psychologists are self-employed. In a field that has
limited job prospects for those with a bachelor’s degree, competition for
admission to graduate programs is high. Those with a doctoral degree will
find the best job prospects in the field, particularly with a focus in a sub-field
such as health. For those seeking a master’s degree, job prospects are best in
industrial-organizational psychology. Though the job outlook for psychology
is good, the number of advanced degrees conferred is growing at 15 percent
(2008–09 to 2013–14).
Be sure to consider all the possible paths to reach your goals, such as Doctor
of Medicine in Psychiatry, a Master’s in Social Work for counseling, or
pursuing an advanced degree in education with certification in counseling.
Degrees Offered in Psychology
Students in clinical psychology who wish for a practitioner-based degree with
less focus on research can pursue the PsyD (Doctor of Psychology), while
students with more research-focused or teaching interests can pursue a PhD in
many of the fields of psychology. Both degrees take around five years to
complete and are highly competitive. Some students choose to pursue their
clinical psychology interests by earning a Master’s in Social Work (MSW).
Social workers are licensed after completing their MSW program from a
Council on Social Work Education (CSWE) accredited program (usually
about two years long) and passing their state’s Association of Social Work
Boards exam. Students should think carefully about their interests and career
goals before selecting a program.
Students can also earn a terminal MS degree in their respective field of
psychology (clinical, school, etc.), usually within two to three years; however
as with most professions, the higher you go, the more careers open up to you.
Graduate work in counseling psychology usually culminates in either a PhD
or an EdD, both of which take around five years to complete. The PhD is
more research-intensive than the EdD, and both are slightly less academically
rigorous than the PhD or PsyD in clinical psychology.
For school psychology the minimum required degree tends to be a master’s
from a state-approved, two-year school psychology program with at least one
year of internship experience. Many states require a more research-heavy
Educational Specialist (EdS) degree, and a good number of school
psychologists also hold doctorate degrees.
You can find more detailed information to guide you on the right path from
these trade organization websites.
TRADE ORGANIZATIONS YOU SHOULD KNOW
American
Psychological
The American Psychological Association offers
information on all areas within the field.
Association
apa.org
Association
for
Psychological
Science
The Association for Psychological Science publishes news,
research, and journals and promotes scientific research
within the field of psychology.
psychologicalscience.org
American
Counseling
Association
The American Counseling Association offers information
on all areas within the field, including information on state
certification.
counseling.org
National
Association of
School
Psychologists
(NASP)
Official website of the NASP, dedicated to sharing
resources, studies, and strategies in order to help the public
and policymakers recognize the effects of students’ mental
health on their development, as well as the importance of
school psychological services.
nasponline.org
Association of Contains information about state licensing requirements.
State and
Provincial
Psychology
Boards
asppb.org
General graduate school requirements:
•
Bachelor’s degree from an accredited college or university
•
Official transcript(s) from all colleges or universities attended
•
GRE General Test scores (different programs require different
minimum scores)
•
TOEFL score (if necessary)
•
Academic letters of recommendation
•
Letter of intent or statement of purpose
•
Application forms
•
Application fee
Some degree programs will also require:
•
GRE Subject Test: Psychology
•
Interview
PUBLIC AFFAIRS AND POLICY
Public affairs is an umbrella that unites public policy and public
administration, drawing upon the fields of political science and economics, to
promote and advance policies and solutions that seek to address the public
good. For those who like to keep their opinions to themselves, note that public
administration is considered a non-partisan environment focused on method
and historical context. Public policy discussions, on the other hand, are
inherently partisan, as those involved seek to advance their agenda and view
of the world as the “rule of the day.”
Job outlook is good, but the number of advanced degrees is growing faster
than projected job growth. Historically, advanced degrees led to government
jobs, but many graduates now work in think tanks, as lobbyists, in academia,
for unions or labor relations groups, and in other non-profit and community
organizations. Given the economic crises faced by many state and local
governments (which employ about 8.3 million people), be sure to keep
options open when seeking employment, especially considering the growing
popularity of the field. The number of advanced degrees conferred has grown
by 31 percent in just five years (2008–09 to 2013–14).
TRADE ORGANIZATIONS YOU SHOULD KNOW
American Society
for Public
Administration
The American Society for Public Administration has a
wealth of information on everything from the latest
policy-making decisions and resource centers to job
listings.
aspanet.org
Association for
Public Policy
Analysis and
Management
The Association for Public Policy Analysis and
Management has information on conferences,
internships, educational programs, jobs, joint degrees,
and awards.
appam.org
National Academy The National Academy for Public Administration is
of Public
committed to monitoring and improving governance
Administration
systems of all kinds.
napawash.org
Network of
Schools of Public
Policy, Affairs,
and
Administration
Accredits schools of public affairs, including those
with dual accreditation. For example, business schools
like Willamette University are accredited by both
AACSB and NASPAA.
naspaa.org
Typical Admissions Requirements
There are no major requirements necessary to apply for advanced degrees in
public policy or administration. Many students have at least one year of work
experience prior to starting their program. For public policy, helpful
background coursework includes economics, statistics, or college-level math.
General graduate school requirements:
•
Bachelor’s degree from an accredited college or university
•
Official transcript(s) from all colleges or universities attended
•
GRE General Test scores (different programs require different
minimum scores)
•
TOEFL score (if necessary)
•
Letters of recommendation
•
Letter of intent or statement of purpose
•
Application forms
•
Application fee
Some degree programs will also require:
•
Work experience
SOCIAL SCIENCES
Social sciences encompass the academic study of fields that fall outside of the
natural sciences and focus on society, including the study of groups,
organizations, institutions, social and economic systems, cultures, and
governments. These disciplines adopt scientific method, with both
quantitative and qualitative analysis geared to social understanding and
improvement.
As globalization creates more complex economies, immigration and social
media bring more cultures together, and political systems shift to reflect
changes in society, the importance of the social sciences is perhaps greater
than ever before.
While the employment outlook for social sciences is competitive in places
like history and economics, many social sciences are experiencing much
faster than average growth. This is somewhat reflected in the number of
candidates receiving an advanced degree, which has grown by 12 percent
(2008–09 to 2013–14).
TRADE ORGANIZATIONS YOU SHOULD KNOW
American
The American Anthropological Association has offered
Anthropological anthropology professionals support, information, and
Association
services since 1902.
aaanet.org
American
Planning
Association
The American Planning Association has advice on
planning in urban and rural areas as well as fellowship
and conference information.
planning.org
American
Political
Science
Association
More than 15,000 members in more than 80 countries
share knowledge, professional advice and advancement,
and a supportive environment conducive to the
professional study of politics.
apsanet.org
American
Sociological
Association
Information for sociologists, students, and the general
public including job opportunities, research grants, and
newly-published reports from members.
asanet.org
International
Economic
Development
Council
Offers information and services for those interested in
economic development.
iedconline.org
International
Studies
Association
The International Studies Association promotes
international affairs research and education.
isanet.org
Typical Admissions Requirements
While many advanced degree programs do not require specific majors or
coursework, many programs recommend background in the area. In addition,
programs like anthropology, international economics, and international
relations require foreign language proficiency. For fields involving math and
research, some coursework in statistics will be helpful background to your
advanced studies as well. When making your application to-do list or
calendar, be sure to note any special application requirements in advance,
especially things like work experience or foreign language requirements,
though some programs may allow you to study a language while working
toward your degree.
General graduate school requirements:
•
Bachelor’s degree from an accredited college or university
•
Official transcript(s) from all colleges or universities attended
•
GRE General Test scores (different programs require different
minimum scores)
•
TOEFL score (if necessary)
•
Academic letters of recommendation
•
Letter of intent or statement of purpose
•
Application forms
•
Application fee
Some degree programs will also require:
•
Interview
•
Relevant work experience
•
Supplemental essays or writing sample
•
Proficiency in a foreign language
SOCIAL WORK
Social workers collaborate with other human services professionals to look
for solutions to the complex problems of modern society. While some social
workers opt for counseling or clinical practices, others work in public policy
and administration, research, or teaching. Because social workers face
society’s most challenging problems, working in this vital field takes a lot of
effort, a lot of patience, and most of all, lots of passion.
Master’s degree programs in social work vary widely in scope and specialty.
Some programs focus on methodology and public policy, while others are
more clinically focused, preparing professionals for a direct practice in
psychotherapy. Still others provide students with the background they need
for a career in public and non-profit social service agencies, or for social
planning and social change. When you are choosing a program, it is important
to consider where you can get training that is in line with your larger career
goals. Upon entering some programs, students are required to choose a
specialty, such as mental health, employee assistance, aging, health care,
corrections, and child welfare.
The job outlook for social workers is good, growing faster than the national
average, particularly for those interested in aging populations, rural settings,
or working with substance abuse programs. The number of advanced degrees
conferred has grown 31 percent in just a few short years between 2008–09
and 2013–14. According to the Council on Social Work Education, women
dominate this field, making up about 86 percent of master’s degree
enrollment, while historically underrepresented groups comprise about 37
percent of full-time enrollment and 40 percent of part-time enrollment.
TRADE ORGANIZATIONS YOU SHOULD KNOW
American Board of
Features job postings, newsletters, and resources for
Examiners in
students of social work.
Clinical Social Work
abecsw.org
American
Counseling
Association
The American Counseling Association offers
information on all areas within the field, including
information on state certification.
counseling.org
Association of Social A professional association that regulates social
Work Boards
work, and develops and maintains the licensing
exam.
aswb.org
National Association The largest member organization of professional
of Social Workers
social workers, offering networking, advocacy,
books and journals.
socialworkers.org
Typical Admissions Requirements
While a BSW is not required for admission to social work programs, some
programs allow enrollees with a BSW to receive advanced standing, thereby
shortening the amount of fieldwork and coursework you are required to
complete.
Many students entering graduate programs in social work have majored in
social work, psychology, or public policy. Otherwise, coursework in social
and biological sciences will be useful. Some basic knowledge of statistics and
research methodologies will also be beneficial to graduate students in social
work.
General graduate school requirements:
•
Bachelor’s degree from an accredited college or university
•
Official transcript(s) from all colleges or universities attended
•
GRE General Test scores (different programs require different
minimum scores)*
•
TOEFL score (if necessary)
•
Letters of recommendation
•
Letter of intent or statement of purpose
•
Application forms
•
Application fee
*Some social work programs accept the Miller Analogy Test in lieu of GRE
Scores.
Some degree programs will also require:
•
Interview
•
Work experience (paid or volunteer)
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